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On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Serge Bogdanovich;  Alexander Ermolitski — 2004

Open Mathematics

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 two basic...

Deformations of structures, embedding of a Riemannian manifold in a Kählerian one and geometric antigravitation

Alexander A. Ermolitski — 2007

Banach Center Publications

Tubular neighborhoods play an important role in modern differential topology. The main aim of the paper is to apply these constructions to geometry of structures on Riemannian manifolds. Deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold are considered in section 1. In section 2, this approach is used to obtain a Kählerian structure on the corresponding normal tubular neighborhood of the null section in the tangent bundle TM of a smooth manifold...

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