Cheeger Gromoll type metrics on the tangent bundle

Details Cheeger Gromoll type metrics on the tangent bundle Cheeger Gromoll type metrics on the tangent bundle

2006-09-30

arxiv.org/abs/math/0610028v1

Mathematics

Differential Geometry

9 pages. to appear in Proceedings of fifth international symposium BioMathsPhys, Iasi, June 16-17, 2006

Scientific paper

In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a Riemannian manifold $M$ which generalizes the Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to $T(M)$ a structure of locally conformal almost K\"ahlerian manifold. We found conditions under which $T(M)$ is almost K\"ahlerian, locally conformal K\"ahlerian or K\"ahlerian or when $T(M)$ has constant sectional curvature or constant scalar curvature.

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