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Unit tangent bundle
About: Unit tangent bundle is a research topic. Over the lifetime, 1056 publications have been published within this topic receiving 15845 citations.
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TL;DR: In this article, the covariant derivatives of the covector fields and killing vector fields with respect to the synectic lift a in a the Riemannian manifold to its tangent bundle are investigated.
Abstract: The purpose of this paper is to investigate applications the covariant derivatives of the covector fields and killing vector fields with respect to the synectic lift a in a the Riemannian manifold to its tangent bundle, where Cg-complete lift of the Riemannian metric, Va-vertical lift of the symmetric tens field of type (0,2) in Mn .
1 citations
TL;DR: In this paper, the authors studied the unoriented cobordism classes of closed smooth manifolds whose tangent bundles admit nilpotent bundle endomorphisms and showed that the structure group of a tangent bundle τ(M) reduces to the group of matrices of the form (# °), A e GLn(R), B G End(iΓ).
Abstract: This paper studies the unoriented cobordism classes of closed smooth manifolds whose tangent bundles admit nilpotent bundle endomorphisms. 1. Introduction. An almost tangent manifold is a smooth (differentiable of class C00) manifold M2n for which the structure group of its tangent bundle τ(M) reduces to the group of matrices of the form (# °), A e GLn(R), B G End(iΓ). The study of these manifolds is motivated by the observation that tangent manifolds have this property, i.e., if Nn is a smooth manifold and E2n is the total space of τ(N), then E2n (a tangent manifold) is an almost tangent manifold. Note that if M 2" is almost tangent, then the matrix
1 citations
01 Jan 2009
TL;DR: In this article, the authors present some aspects from the study of geometric structures of natural lift type on the tangent bundle of a Riemannian manifold and present the basic constructions leading to the almost Hermitian structures of diagonal type.
Abstract: We present some aspects from the study of geometric structures of natural lift type on the tangent bundle of a Riemannian manifold. After presenting, in the first two sections, the basic constructions leading to the almost Hermitian structures of diagonal type, we
1 citations
TL;DR: In this article , the authors explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle, and prove some theorems on the curvature tensor and the projective curvatures of a SISKIAN manifold with respect to the Riemannian connection.
Abstract: The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle was established. Some theorems on the curvature tensor and the projective curvature tensor of a Sasakian manifold with respect to the quarter-symmetric metric connection to its tangent bundle were proved. Finally, locally ϕ-symmetric Sasakian manifolds with respect to the quarter-symmetric metric connection to its tangent bundle were studied.
1 citations