Almost Hermitian structures on tangent bundles

Para-Kahler tangent bundles of constant para-holomorphic sectional curvature

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

New structures on the tangent bundles and tangent sphere bundles

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifold M which generalizes Sasaki metric and 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. This is the natural generalization of the well known almost Kählerian structure on T (M). W...

Hermitian and quaternionic Hermitian structures on tangent bundles

We review the theory of quaternionic Kähler and hyperkähler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure. With an extra almost Hermitian structure on M it is possible to find a quaternionic Hermitian structure on TM , which is quaternionic Kähler if, and only if, D ...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

Tangent Bundles with Sasaki Metric and Almost Hypercomplex Pseudo-hermitian Structure

The tangent bundle as a 4n-manifold is equipped with an almost hypercomplex pseudo-Hermitian structure and it is characterized with respect to the relevant classifications. A number of 8-dimensional examples of the considered type of manifold are received from the known explicit examples in that manner.