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.

Fano 5-folds with nef tangent bundles and Picard numbers greater than one

Abstract: We prove that smooth Fano 5-folds with nef tangent bundles and Picard numbers greater than one are rational homogeneous manifolds.

Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles

Abstract: In this paper we give some examples of almost para-hyperhermitian structures on the tangent bundle of an almost product manifold, on the product manifold $M\times\mathbb{R}$, where $M$ is a manifold endowed with a mixed 3-structure and on the circle bundle over a manifold with a mixed 3-structure.

Differential and Geometric Structure for the Tangent Bundle of a Projective Limit Manifold.

Abstract: The tangent bundle of a wide class of Frechet manifolds is studied he- re. A vector bundle structure is obtained with structural group a topological subgroup of the general linear group of the fiber type. Moreover, basic geo- metric results, known form the classical case of finite dimensional manifolds, are recovered here: Connections can be defined and are characterized by a generalized type of Christoffel symbols while, at the same time, parallel di- splacements of curves are possible despite the problems concerning differen- tial equations in Frechet spaces.

A Frobenius Theorem on Convenient Manifolds

Abstract: A Frobenius Theorem for finite dimensional, involutive subbundles of the tangent bundle of a convenient manifold is proved. As first key applications Lie’s second fundamental theorem and Nelson’s theorem are treated in the convenient case.