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Norden structures on cotangent bundles

  • Antonella NanniciniEmail author
Article
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Abstract

We study extensions of Norden structures on manifolds to their generalized tangent bundles and to their cotangent bundles. In particular, by using methods of generalized geometry, we prove that the cotangent bundle of a complex Norden manifold (MJg) admits a structure of Norden manifold, \((T^{\star }(M),{\tilde{J}}, \tilde{g})\). Moreover if (MJg) has flat natural canonical connection then \({\tilde{J}}\) is integrable, that is \((T^{\star }(M),{\tilde{J}}, {\tilde{g}})\) is a complex Norden manifold. Finally we prove that if (MJg) is Kähler Norden flat then \((T^{\star }(M),{\tilde{J}}, {\tilde{g}})\) is Kähler Norden flat.

Keywords

Complex manifolds Cotangent bundles Generalized geometry Norden manifolds 

Mathematics Subject Classification

53C15 53C56 53D18 53D05 

Notes

Acknowledgements

The author’s research was partially supported by the following grants of the Italian Ministry of Education (MIUR): PRIN Varietà reali e complesse (2010NNBZ78) and by GNSAGA of INDAM.

Compliance with ethical standards

Conflict of interest

The author states that there is no conflict of interest.

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Copyright information

© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Informatica “U. Dini”FlorenceItaly

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