Displaying similar documents to “Deformations of structures, embedding of a Riemannian manifold in a Kählerian one and geometric antigravitation”

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

Mariusz Plaszczyk (2015)

Annales UMCS, 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 → JrTM between the r-th order prolongation JrTM of tangent TM and the r-th order prolongation JrT M of cotangent TM bundles of M. Further we describe all base preserving vector bundle maps DM(g) : JrTM → JrT* M depending...

Anti-invariant Riemannian submersions from almost Hermitian manifolds

Bayram Ṣahin (2010)

Open Mathematics

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We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for...

On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Serge Bogdanovich, Alexander Ermolitski (2004)

Open Mathematics

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Some results concerning almost hyperHermitian structures are considered, using the notions of the canonical connection and the second fundamental tensor field h of a structure on a Riemannian manifold which were introduced by the second author. With the help of any metric connection ∇ ˜ on an almost Hermitian manifold M an almost hyperHermitian structure can be constructed in the defined way on the tangent bundle TM. A similar construction was considered in [6], [7]. This structure includes...

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

Similarity:

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...

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...