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Cheeger Gromoll type metrics on the tangent bundle

Marian Ioan Munteanu
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Abstract

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 Kählerian manifold. We found conditions under which $T(M)$ is almost Kählerian, locally conformal Kählerian or Kählerian or when $T(M)$ has constant sectional curvature or constant scalar curvature.

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Marian Ioan Munteanu. 2006-09-30. Cheeger Gromoll type metrics on the tangent bundle. https://arxiv.org/abs/math/0610028

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