# On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Serge Bogdanovich; Alexander Ermolitski

Open Mathematics (2004)

- Volume: 2, Issue: 5, page 615-623
- ISSN: 2391-5455

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topSerge 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 -

## References

top- [1] P. Dombrowski: “On the Geometry of the Tangent Bundle”, J. Reine und Angew. Math., Vol. 210, (1962), pp. 73–88. Zbl0105.16002
- [2] A.A. Ermolitski: Riemannian manifolds with geometric structures, BSPU, Minsk, 1998 (in Russian). Zbl0812.53046
- [3] A. Gray and L.M. Herwella: “The sixteen classes of almost Hermitian manifolds and their linear invariants”, Ann. Mat. pura appl., Vol. 123, (1980), pp. 35–58. http://dx.doi.org/10.1007/BF01796539 Zbl0444.53032
- [4] D. Gromoll, W. Klingenberg and W. Meyer: Riemannsche geometrie im großen, Springer, Berlin, 1968 (in German). Zbl0155.30701
- [5] O. Kowalski: Generalized symmetric space, Lecture Notes in Math, Vol. 805, Springer-Verlag, 1980. Zbl0431.53042
- [6] F. Tricerri: “Sulle varieta dotate di due strutture quusi complesse linearmente indipendenti”, Riv. Mat. Univ. Parma, Vol. 3, (1974), pp. 349–358 (in Italian). Zbl0344.53022
- [7] F. Tricerri: “Conessioni lineari e metriche Hermitiene sopra varieta dotate di due strutture quasi complesse”, Riv. Mat. Univ. Parma, Vol. 4, (1975), pp. 177–186 (in Italian).

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