Comptes Rendus
no. 19-20
Differential Geometry
Classes of compact non-Kähler manifolds
[Classes de variétés compactes non Kähleriennes]

Présenté par : Jean-Pierre Demailly

Lucia Alessandrini1
1 Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze, 43124 Parma, Italy
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1089-1092.

Nous étudions différentes classes de variétés compactes non Kähleriennes, dont beaucoup existent déjà dans la littérature, qui se caractérisent par des formes et des courants positifs. Le but de la note est de présenter une vue dʼensemble mettant en évidence les liens entre les différentes classes et pointant quelques problèmes intéressants.

We study various classes of compact non-Kähler manifolds, many of which already exist in the literature, which are characterized by positive forms and currents. The goal of the note is to present an overview that highlights the links between the various classes and raises some interesting problems.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.09.001

Lucia Alessandrini 1

1 Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze, 43124 Parma, Italy 
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Lucia Alessandrini. Classes of compact non-Kähler manifolds. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1089-1092. doi : 10.1016/j.crma.2011.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.09.001/

[1] L. Alessandrini; M. Andreatta Closed transverse (p,p)-forms on compact complex manifolds, Compositio Math., Volume 61 (1987), pp. 181-200 (Erratum)

[2] L. Alessandrini; G. Bassanelli Small deformations of a class of compact non-Kähler manifolds, Proc. AMS, Volume 109 (1990), pp. 1059-1062

[3] L. Alessandrini; G. Bassanelli Compact p-Kähler manifolds, Geometriae Dedicata, Volume 38 (1991), pp. 199-210

[4] P. Deligne; P. Griffiths; J. Morgan; D. Sullivan Real homotopy theory of Kähler manifolds, Invent. Math., Volume 29 (1975), pp. 245-274

[5] N. Egidi Special metrics on compact complex manifolds, Differential Geom. Appl., Volume 14 (2001), pp. 217-234

[6] J. Fu; S.T. Yau A note on small deformations of balanced manifolds | arXiv

[7] P. Gauduchon Le théoreme de lʼexcentricité nulle, C. R. Acad. Sci. Paris, Ser. A, Volume 285 (1977), pp. 387-390

[8] M. Gromov Pseudo holomorphic curves in symplectic manifolds, Invent. Math., Volume 82 (1985), pp. 307-347

[9] R. Harvey; A.W. Knapp Positive (p,p)-forms, Wirtingerʼs inequality and currents, Proc. Tulane Univ. 1972–1973, Marcel Dekker, New York, 1974, pp. 43-62

[10] R. Harvey; H.B. Lawson An intrinsic characterization of Kähler manifolds, Invent. Math., Volume 74 (1983), pp. 169-198

[11] D. Mc Duff; D. Salamon Introduction to Symplectic Topology, Oxford Math. Monograph, Oxford Sci. Publ., 1995

[12] M.L. Michelson On the existence of special metrics in complex geometry, Acta Math., Volume 143 (1983), pp. 261-295

[13] D. Popovici Limits of projective manifolds under holomorphic deformations | arXiv

[14] D. Popovici Stability of strongly Gauduchon manifolds under modifications | arXiv

[15] D. Popovici Deformation openness and closedness of various classes of compact complex manifolds: examples | arXiv

[16] D. Sullivan Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math., Volume 36 (1976), pp. 225-255

[17] J. Varouchas Propriétés cohomologiques dʼune classe de variétés analytiques complexes compactes, Séminaire dʼanalyse P. Lelong, P. Dolbeault, H. Skoda, années 1983–1984, Lecture Notes in Math., vol. 1198, Springer, Berlin, 1986, pp. 233-243

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