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Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
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01 Jan 2007
TL;DR: In this article, the authors studied the geometry of tangent bundle of a Finsler manifold endowed with Sasaki metric and obtained some results, such as the vertical lift of any vector is divergence-free or equivalently, such that the horizontal distribution is minimal in the tangent of the slit tangent bundles.
Abstract: . In this paper we study the geometry of tangent bundle of a Finslermanifold endowed with Sasaki metric and obtain some results. We characterize theRiemannian manifold as the Finsler manifold such that the vertical lift of any vectorfield is divergence-free or equivalently, such that the horizontal distribution is minimalin the tangent bundle of the slit tangent bundle, and prove that the almost complexstructure on the slit tangent bundle is integrable if and only if the base manifold haszero flag curvature. In that case, the slit tangent bundle is K¨ahlerian. We also provethat the slit tangent bundle is locally symmetric if and only if the base manifold islocally Euclidean. Our results generalize the corresponding results for the Riemanniansetting in the literature. 1. IntroductionThe geometry of tangent bundle or tangent sphere bundle of a Riemannianmanifold has been well developed. In the general case, however, the geometry oftangent bundle or the indicatrix bundle of a Finsler manifold has not been studiedat the same pace. Several people have made some fundamental contributions tothis subject from various points of view. For instance, Hasegawa, Yamauchi,and Shimada proved that the indicatrix bundle of a Finsler manifold (M,F) withthe induced almost contact metric structure is Sasakian if and only if (M,F) is ofconstant flag curvature 1 [8], while Bejancu and Farran obtained that (M,F)
7 citations
TL;DR: In this paper, the authors define Wick-rotations by considering pseudo-Riemannian manifolds as real slices of a holomorphic Riemannians manifold and derive new results regarding the existence, and non-existence, of such Wickrotations.
7 citations
7 citations
TL;DR: In this paper, it was shown that the determinants of the correlation functions of the generalized bc-system are given as pullbacks of the non-Abelian theta divisor.
Abstract: It is shown that the determinants of the correlation functions of the generalized bc-system introduced recently are given as pullbacks of the non-Abelian theta divisor.
7 citations
Journal Article•
TL;DR: In this paper, a diagonal lift Dg of Riemannian metric g of manifold Mn to the tangent bundle of order two denoted by T2Mn of Mn was defined.
Abstract: In this paper we define a diagonal lift Dg of Riemannian metric g of manifold Mn to the tangent bundle of order two denoted by T2Mn of Mn, we associate to Dg its Levi-civita connection of T2 M and we investigate applications of the diagonal lifts in the killing vectors and geodesics.
7 citations