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## Open Mathematics

2004 | 2 | 5 | 615-623
Tytuł artykułu

### On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

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EN
Abstrakty
EN
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.
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EN
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Tom
Numer
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615-623
Opis fizyczny
Daty
wydano
2004-10-01
online
2004-10-01
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autor
autor
Bibliografia
• [1] P. Dombrowski: “On the Geometry of the Tangent Bundle”, J. Reine und Angew. Math., Vol. 210, (1962), pp. 73–88.
• [2] A.A. Ermolitski: Riemannian manifolds with geometric structures, BSPU, Minsk, 1998 (in Russian).
• [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
• [4] D. Gromoll, W. Klingenberg and W. Meyer: Riemannsche geometrie im großen, Springer, Berlin, 1968 (in German).
• [5] O. Kowalski: Generalized symmetric space, Lecture Notes in Math, Vol. 805, Springer-Verlag, 1980.
• [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).
• [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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