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On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

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Bogdanovich S., Ermolitski A.

Open Mathematics

2004

tom 2

nr 5

615-623

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 $$\tilde \nabla $$ 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 anticommutative almost Hermitian structures for which the second fundamental tensor fields h 1 and h 2 are computed. It allows us to consider various classes of almost hyperHermitian structures on TM. In particular, there exists an infinite-dimensional set of almost hyperHermitian structures on TTM where M is any Riemannian manifold.

Ograniczanie wyników

1 Open Mathematics

1 Bogdanovich S.

1 Ermolitski A.

1 2004

Wyniki wyszukiwania

On almost hyperHermitian structures on Riemannian manifolds and tangent bundles