Cheeger Gromoll type metrics on the tangent bundle

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.

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

Cited by in corpus (3)

• Conformally flat tangent bundles with general natural lifted metrics
• The Sectional Curvature of the Tangent Bundles with General Natural Lifted Metrics
• Differential as a harmonic morphism with respect to Cheeger--Gromoll type metrics