Displaying similar documents to “Statistical structures on tangent bundles.”

On the geometry of tangent bundles with the metric II+III

A. Gezer, O. Tarakci, A. A. Salimov (2010)

Annales Polonici Mathematici

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The main purpose of this paper is to investigate some relations between the flatness or locally symmetric property on the tangent bundle TM equipped with the metric II+III and the same property on the base manifold M and study geodesics by means of the adapted frame on TM.

Double vector bundles and duality

Katarzyna Konieczna, Pawel Urbański (1999)

Archivum Mathematicum

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The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given.

Varieties with generically nef tangent bundles

Thomas Peternell (2012)

Journal of the European Mathematical Society

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We study various "generic" nefness and ampleness notions for holomorphic vector bundles on a projective manifold. We apply this in particular to the tangent bundle and investigate the relation to the geometry of the manifold.

On para-Nordenian structures

Arif A. Salimov, Filiz Agca (2010)

Annales Polonici Mathematici

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The aim of this paper is to investigate para-Nordenian properties of the Sasakian metrics in the cotangent bundle.

The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds

Jan Kurek, Włodzimierz M. Mikulski (2015)

Annales UMCS, Mathematica

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If (M,g) is a Riemannian manifold, we have the well-known base preserving vector bundle isomorphism TM ≅ T∗ M given by υ → g(υ,−) between the tangent TM and the cotangent T∗ M bundles of M. In the present note, we generalize this isomorphism to the one T(r)M ≅ Tr∗ M between the r-th order vector tangent T(r)M = (Jr(M,R)0)∗ and the r-th order cotangent Tr∗ M = Jr(M,R)0 bundles of M. Next, we describe all base preserving vector bundle maps CM(g) : T(r)M → Tr∗ M depending on a Riemannian...

The natural transformations between r-th order prolongation of tangent and cotangent bundles over Riemannian manifolds

Mariusz Plaszczyk (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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If (M, g) is a Riemannian manifold then there is the well-known base preserving vector bundle isomorphism TM → T*M given by v → g(v, –) between the tangent TM and the cotangent T*M bundles of M. In the present note first we generalize this isomorphism to the one JrTM → JrT*M between the r-th order prolongation JrTM of tangent TM and the r-th order prolongation JrT*M of cotangent T*M bundles of M. Further we describe all base preserving vector bundle maps DM(g) : JrTM → JrT*M depending...