Natural Ricci Solitons on Tangent and Unit Tangent Bundles

Remarks on η-Einstein unit tangent bundles

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the η-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is ηEinstein manifold if and only if base manifold is the space of constant sectional c...

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...

Tangent and Cotangent Bundles

of subsets of TM: Note that i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU =  1 (R) 2 : ii) If we de…ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so  (p; Xp) = ( (p); F ( Xp)); and  1 = ( 1 ; F 1 ): Now take  1 (U);  1 (V ) 2 and suppos...

Tangent and Cotangent Bundles

i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU =  1 (R) 2 . ii) If we de…ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so  (p; Xp) = ( (p); F ( Xp)); and  1 = ( 1 ; F 1 ). Now take  1 (U);  1 (V ) 2 and suppose (p; Xp) 2  1 (U)\  1 (V ...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles