Generalized Sasaki metrics on tangent bundles

Izu Vaisman

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arXiv · 1312.4279

Generalized Sasaki metrics on tangent bundles

Izu Vaisman

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Abstract

We define a class of metrics that extend the Sasaki metric of a tangent manifold of a Riemannian manifold. The new metrics are obtained by the transfer of the generalized (pseudo-)Riemannian metrics of the pullback of the big tangent bundle of a manifold to the tangent manifold. We obtain the expression of the transferred metric and we define a canonical, metric connection with torsion. We calculate the torsion, curvature and Ricci curvature of this connection and give a few applications of the results. We also discuss the transfer of generalized complex and generalized Kaehler structures.

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BibTeX RIS

Izu Vaisman. 2013-12-16. Generalized Sasaki metrics on tangent bundles. https://arxiv.org/abs/1312.4279

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