On almost hyperHermitian structures on Riemannian manifolds and tangent bundles |
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Authors: | Serge A Bogdanovich Alexander A Ermolitski |
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Institution: | (1) Cathedra of Mathematics, Belorussian State Pedagogical University, st. Sovietskaya 18, 220050 Minsk, Belarus |
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Abstract: | 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 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. |
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Keywords: | Riemannian manifolds almost hyperHermitian structures tangent bundle |
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