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

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...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

ON THE LIFTS OF SEMI-RIEMANNIAN METRICS

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

Local Symmetry of Unit Tangent Sphere Bundle With g- Natural Almost Contact B-Metric Structure

We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...