publications.md

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publications	Publications	active	abstract archiveprefix arxivid author eprint keywords page title URL id type issued Let $V$ be a complex orthogonal vector space and $S$ an irreducible $C\!\ell(V)$-module. A supertranslation algebra is a Z-graded Lie superalgebra $\mathfrak{m}=\mathfrak{m}_{-2}+\mathfrak{m}_{-1}=V+(S+...+S)$ whose bracket $[.,.]|_{\mathfrak{m}_{-1}\otimes \mathfrak{m}_{-1}}$ is $\mathfrak{so}(V)$-invariant and non-degenerate. We consider the maximal transitive prolongations in the sense of Tanaka of supertranslation algebras. We prove that they are finite-dimensional for $\dim V\geq 3$ and classify them in terms of super-Poincaré algebras and appropriate $\Bbb Z$-gradations of simple Lie superalgebras. arXiv 1212.1826 family given Altomani A. family given Santi A. 1212.1826 Mathematical Physics,Rings and Algebras 1-25 Classification of maximal transitive prolongations of super-Poincaré algebras http://arxiv.org/abs/1212.1826 Altomani2012 article-journal date-parts 2012 12 abstract archiveprefix arxivid author eprint keywords page title URL id type issued We consider isometric immersions in arbitrary codimension of three-dimensional strongly pseudoconvex pseudo-hermitian CR manifolds into the Euclidean space $\mathbb{R}^n$ and generalize in a natural way the notion of associated family. We show that the existence of such deformations turns out to be very restrictive and we give a complete classification. arXiv 1202.4624 family given Altomani A. family given Lawn M.-A. 1202.4624 Differential Geometry 1-15 Associated Families of Immersions of Three Dimensional CR Manifolds in Euclidean Spaces http://arxiv.org/abs/1202.4624 Altomani2012a article-journal date-parts 2012 2 abstract archiveprefix arxivid author eprint keywords page title URL toappear id type issued Let $(V,(.,.))$ be a pseudo-Euclidean vector space and $S$ an irreducible $C\!\ell(V)$-module. An extended translation algebra is a graded Lie algebra $\mathfrak{m}=\mathfrak{m}_{-2}+\mathfrak{m}_{-1}=V+S$ with bracket given by $([s,t],v) = \beta(v\cdot s,t)$ for some nondegenerate $\mathfrak{so}(V)$-invariant reflexive bilinear form $\beta$ on $S$. An extended Poincaré structure on a manifold $M$ is a regular distribution $\mathcal D$ of depth 2 whose Levi form $L_x: \mathcal D_x\wedge\mathcal D_x\rightarrow T_xM/\mathcal D_x$ at any point $x\in M$ is identifiable with the bracket $[.,.]: S\wedge S\rightarrow V$ of a fixed extended translation algebra $\mathfrak m$. The classification of the standard maximally homogeneous manifolds with an extended Poincaré structure is given, in terms of Tanaka prolongations of extended translation algebras and of appropriate gradations of real simple Lie algebras. arXiv 1201.0555 family given Altomani A. family given Santi A. 1201.0555 Differential Geometry,Mathematical Physics 1-23 Tanaka structures modeled on extended Poincaré algebras http://arxiv.org/abs/1201.0555 Indiana Univ. Math. J. Altomani2012b article-journal date-parts 2012 1 abstract archiveprefix arxivid author eprint keywords page title URL toappear id type issued Using a bigraded differential complex depending on the CR and pseudohermitian structure, we give a characterization of three-dimensional strongly pseudoconvex pseudo-hermitian CR-manifolds isometrically immersed in Euclidean space $\mathbb{R}^n$ in terms of an integral representation of Weierstrass type. Restricting to the case of immersions in $\mathbb{R}^4$, we study harmonicity conditions for such immersions and give a complete classification of CR-pluriharmonic immersions. arXiv 1106.2962 family given Altomani A. family given Lawn M.-A. 1106.2962 Complex Variables,Differential Geometry 1-24 Isometric and CR pluriharmonic immersions of three dimensional CR manifolds in Euclidean spaces http://arxiv.org/abs/1106.2962 Hokkaido Math. J. Altomani2011 article-journal date-parts 2011 6 abstract archiveprefix arxivid author eprint keywords page title URL toappear id type issued We consider a class of compact homogeneous CR manifolds, that we call $\mathfrak n$-reductive, which includes the orbits of minimal dimension of a compact Lie group $K_0$ in an algebraic homogeneous variety of its complexification $K$. For these manifolds we define canonical equivariant fibrations onto complex flag manifolds. The simplest example is the Hopf fibration $S^3\to\mathbb{CP}^1$. In general these fibrations are not $CR$ submersions, however they satisfy a weaker condition that we introduce here, namely they are CR-deployments. arXiv 1106.2779 family given Altomani A. family given Medori C. family given Nacinovich M. 1106.2779 Complex Variables,Differential Geometry 1-35 Reductive compact homogeneous CR manifolds http://arxiv.org/abs/1106.2779 Transf. Groups Altomani2011a article-journal date-parts 2011 6 author title container-title issue page scopus_url abstract issn coden DOI abbrev_source_title document_type source mrnumber zblnumber archiveprefix eprint id type issued family given Altomani A. family given Medori C. A characterization of CR quadrics with a symmetry property Journal of Geometric Analysis 22 892-909 http://www.scopus.com/inward/record.url?eid=2-s2.0-84863826419&partnerID=40&md5=91f6d60d8196f519ac8622638badf01e We study CR quadrics satisfying a symmetry property $(\tilde S)$ which is slightly weaker than the symmetry property $(S)$, recently introduced by W. Kaup, which requires the existence of an automorphism reversing the gradation of the Lie algebra of infinitesimal automorphisms of the quadric. We characterize quadrics satisfying the $(\tilde S)$ property in terms of their Levi-Tanaka algebras. In many cases the $(\tilde S)$ property implies the $(S)$ property; this holds in particular for compact quadrics. We also give a new example of a quadric such that the dimension of the algebra of positive-degree infinitesimal automorphisms is larger than the dimension of the quadric. 10506926 JGANE 10.1007/s12220-011-9228-6 J. Geom. Anal. Article Scopus 2927683 06112735 arXiv 1011.3358 Altomani2012892 article-journal date-parts 2012 author title container-title issue page scopus_url abstract issn abbrev_source_title document_type source eprint mrnumber zblnumber id type issued family given Altomani A. family given Hill C. D. family given Nacinovich M. family given Porten E. Holomorphic extension from weakly pseudoconcave CR manifolds Rendiconti del Seminario Matematico dell 'Universita' di Padova 123 69-90 http://www.scopus.com/inward/record.url?eid=2-s2.0-84856140498&partnerID=40&md5=6ba76a51f4eafb1456e828be0e8e50e2 Let $M$ be a smooth locally embeddable CR manifold, having some CR dimension $m$ and some CR codimension $d$. We find an improved local geometric condition on $M$ which guarantees, at a point $p$ on $M$, that germs of CR distributions are smooth functions, and have extensions to germs of holomorphic functions on a full ambient neighborhood of $p$. Our condition is a form of weak pseudoconcavity, closely related to essential pseudoconcavity as introduced in [HN1], Applications are made to CR meromorphic functions and mappings. Explicit examples are given which satisfy our new condition, but which are not pseudoconcave in the strong sense. These results demonstrate that for codimension $d > 1$ there are additional phenomena, which are invisible when $d = 1$. 00418994 Rend. Semin. Mat. Univ. Padova Article Scopus 0903.5318 2683292 1210.32016 Altomani201069 article-journal date-parts 2010 author title container-title issue page scopus_url abstract issn abbrev_source_title document_type source eprint mrnumber zblnumber id type issued family given Altomani A. family given Medori C. family given Nacinovich M. Orbits of real forms in complex flag manifolds Annali della Scuola Normale - Classe di Scienze IX 69-109 http://www.scopus.com/inward/record.url?eid=2-s2.0-83455214186&partnerID=40&md5=a100da7886204358a373e736119295f2 We investigate the CR geometry of the orbits $M$ of a real form $G_0$ of a complex semisimple Lie group $G$ in a complex flag manifold $X = G/Q$. We are mainly concerned with finite type and holomorphic nondegeneracy conditions, canonical $G_0$-equivariant and Mostow fibrations, and topological properties of the orbits. 0391173X Ann. Sc. Norm. Sup. Cl. Sci. Article Scopus 0711.4484 2668874 1198.53051 Altomani201070 article-journal date-parts 2010 author title container-title issue page scopus_url abstract issn abbrev_source_title document_type source eprint mrnumber zblnumber id type issued family given Altomani A. family given Hill C. D. family given Nacinovich M. family given Porten E. Complex vector fields and hypoelliptic partial differential operators Annales de l'Institut Fourier 60 987-1034 http://www.scopus.com/inward/record.url?eid=2-s2.0-77958504834&partnerID=40&md5=f8dadf2101ab9fcbe2c9c613b6ba0b88 We prove a subelliptic estimate Tor systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of $(0,1)$ vector fields satisfies a subelliptic estimate. 03730956 Ann. Inst. Fourier Article Scopus 0807.4857 2680822 1197.35083 Altomani2010987 article-journal date-parts 2010 abstract archiveprefix arxivid author eprint keywords page title URL container-title abbrev_source_title issue mrnumber zblnumber id type issued We consider canonical fibrations and algebraic geometric structures on homogeneous CR manifolds, in connection with the notion of CR algebra. We give applications to the classifications of left invariant CR structures on semisimple Lie groups and of CR-symmetric structures on complete flag varieties. arXiv 0910.4531 family given Altomani A. family given Medori C. family given Nacinovich M. 0910.4531 Complex Variables,Differential Geometry 221-265 On homogeneous and symmetric CR manifolds http://arxiv.org/abs/0910.4531 Bollettino dell'Unione Matematica Italiana (9) Boll. Unione Mat. Ital. 3 2666357 1214.32009 Altomani2009 article-journal date-parts 2010 10 author title container-title issue page scopus_url abstract issn DOI abbrev_source_title document_type source eprint mrnumber zblnumber id type issued family given Altomani A. family given Medori C. family given Nacinovich M. On the topology of minimal orbits in complex flag manifolds Tohoku Mathematical Journal 60 403-422 http://www.scopus.com/inward/record.url?eid=2-s2.0-55949133757&partnerID=40&md5=ad2c354c9a8f956479af246bc9b2e977 We compute the Euler-Poincaré characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold. 00408735 10.2748/tmj/1223057736 Tohoku Math. J. Article Scopus 0709.2608 2453731 1160.57033 Altomani2008403 article-journal date-parts 2008 abstract archiveprefix arxivid author eprint keywords page primaryclass title URL id type issued Let $M$ be an orbit of a real semisimple Lie group $G_0$ acting on a complex a flag manifolds $G/Q$ of its complexification $G$. We study the space of global CR functions on $M$ and characterize those $M$ which are strictly locally CR separable, i.e. those for which global CR functions induce local embeddings in $\Bbb C^n$. arXiv math/0702845 family given Altomani A. 0702845 Complex Variables 1-11 math Global CR functions on parabolic CR manifolds http://arxiv.org/abs/math/0702845 Altomani2007b article-journal date-parts 2007 2 abstract archiveprefix arxivid author eprint keywords page primaryclass title URL id type issued We study, from the point of view of CR geometry, the orbits $M$ of a real form $G_0$ of a complex semisimple Lie group $G$ in a complex flag manifold $G/Q$. In particular we characterize those that are of finite type and satisfy some Levi nondegeneracy conditions. These properties are also graphically described by attaching to them some cross-marked diagrams that generalize those for minimal orbits that we introduced in a previous paper. By constructing canonical fibrations over real flag manifolds, with simply connected complex fibers, we are also able to compute their fundamental group. arXiv math/0611755 family given Altomani A. family given Medori C. family given Nacinovich M. 0611755 Complex Variables,Differential Geometry 1-58 math Orbits of real forms in complex flag manifolds http://arxiv.org/abs/math/0611755 Altomani2006 article-journal date-parts 2006 11 author title container-title issue page scopus_url abstract issn abbrev_source_title document_type source eprint mrnumber zblnumber id type issued family given Altomani A. family given Medori C. On homogeneous CR manifolds and their CR algebras International Journal of Geometric Methods in Modern Physics 3 1199-1214 http://www.scopus.com/inward/record.url?eid=2-s2.0-33750138729&partnerID=40&md5=1711fbfeb2dc0b06af9b37de54329cd1 In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond to geometrical properties for the corresponding manifolds. We also give distinguished equivariant CR fibrations for homogeneous CR manifolds. In the second part of the paper we apply these results to minimal orbits for the action of a real form of a semisimple Lie group $G$ on a flag manifold $G/Q$. 02198878 Int. J. Geom. Methods Mod. Phys. Article Scopus 0510635 2264411 1113.32006 Altomani20061199 article-journal date-parts 2006 author title container-title issue page scopus_url abstract issn abbrev_source_title document_type source eprint mrnumber zblnumber id type issued family given Altomani A. family given Medori C. family given Nacinovich M. The CR structure of minimal orbits in complex flag manifolds Journal of Lie Theory 16 483-530 http://www.scopus.com/inward/record.url?eid=2-s2.0-33746217549&partnerID=40&md5=18319ee3e6f5678d151e300be30f89e6 Let $\^G$ be a complex semisimple Lie group, $Q$ a parabolic subgroup and $G$ a real form of $\^G$. The flag manifold $\^G/Q$ decomposes into finitely many $G$-orbits; among them there is exactly one orbit of minimal dimension, which is compact. We study these minimal orbits from the point of view of CR geometry. In particular we characterize those minimal orbits that are of finite type and satisfy various nondegeneracy conditions, compute their fundamental group and describe the space of their global CR functions. Our main tool are parabolic CR algebras, which give an infinitesimal description of the CR structure of minimal orbits. 09495932 J. Lie Theory Article Scopus 0507272 2248142 1120.32023 Altomani2006483 article-journal date-parts 2006 abstract archiveprefix arxivid author eprint keywords page primaryclass title URL issue container-title abbrev_source_title mrnumber zblnumber id type issued We prove a relation between the $\bar\partial_M$ cohomology of a minimal orbit $M$ of a real form $G_0$ of a complex semisimple Lie group $G$ in a flag manifold $G/Q$ and the Dolbeault cohomology of the Matsuki dual open orbit $X$ of the complexification $K$ of a maximal compact subgroup $K_0$ of $G_0$, under the assumption that $M$ is Levi-flat. arXiv math/0601617 family given Altomani A. 0601617 Complex Variables,Differential Geometry 283-293 math A note on the CR cohomology of Levi-Flat minimal orbits in complex flag manifolds http://arxiv.org/abs/math/0601617 3 Rendiconti dell'Istituto Matematico dell'Università di Trieste Rend. Ist. Mat. Univ. Trieste 2227062 1140.32026 Altomani2006a article-journal date-parts 2005 1 author title container-title issue page scopus_url abstract issn DOI abbrev_source_title document_type source eprint mrnumber zblnumber id type issued family given Altomani A. family given Nacinovich M. Abelian extensions of semisimple graded CR algebras Advances in Geometry 4 433-457 http://www.scopus.com/inward/record.url?eid=2-s2.0-33746235761&partnerID=40&md5=8255a9895e7aa576d8eff8b162433d73 In this paper we take up the problem of describing the CR vector bundles $M$ over compact standard CR manifolds $S$, which are themselves standard CR manifolds. They are associated to special graded Abelian extensions of semisimple graded CR algebras. 1615715X 10.1515/advg.2004.4.4.433 Adv. Geometry Article Scopus 0307184 2096522 1077.32019 Altomani2004433 article-journal date-parts 2004

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