On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Serge Bogdanovich, and Alexander Ermolitski. "On almost hyperHermitian structures on Riemannian manifolds and tangent bundles." Open Mathematics 2.5 (2004): 615-623. <http://eudml.org/doc/268713>.

@article{SergeBogdanovich2004,
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 \[\tilde\{\nabla \}\] 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.},
author = {Serge Bogdanovich, Alexander Ermolitski},
journal = {Open Mathematics},
keywords = {53C15; 53C26},
language = {eng},
number = {5},
pages = {615-623},
title = {On almost hyperHermitian structures on Riemannian manifolds and tangent bundles},
url = {http://eudml.org/doc/268713},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Serge Bogdanovich
AU - Alexander Ermolitski
TI - On almost hyperHermitian structures on Riemannian manifolds and tangent bundles
JO - Open Mathematics
PY - 2004
VL - 2
IS - 5
SP - 615
EP - 623
AB - 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.
LA - eng
KW - 53C15; 53C26
UR - http://eudml.org/doc/268713
ER -