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.
@article{bwmeta1.element.doi-10_2478_BF02475969,
author = {Serge Bogdanovich and Alexander Ermolitski},
title = {On almost hyperHermitian structures on Riemannian manifolds and tangent bundles},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {615-623},
zbl = {1114.53024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475969}
}
Serge Bogdanovich; Alexander Ermolitski. On almost hyperHermitian structures on Riemannian manifolds and tangent bundles. Open Mathematics, Tome 2 (2004) pp. 615-623. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475969/
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