General natural Einstein Kähler structures on tangent bundles

Oproiu, Vasile; Papaghiuc, Neculai

doi:10.1016/j.difgeo.2008.10.017

Cited by 18 publications

(15 citation statements)

References 6 publications

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“…In the next section, following the same techniques as in [3,21,22,[24][25][26], we deform the almost parahyperhermitian structure given above in order to obtain an entire family of structures of this kind on the tangent bundle of an almost para-hermitian manifold. …”

Section: Is An Almost Para-hypercomplex Structure On T M Which Is Parmentioning

confidence: 99%

Para-hyperhermitian structures on tangent bundles

Vîlcu¹

2011

Proc. Estonian Acad. Sci.

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In this paper we construct a family of almost para-hyperhermitian structures on the tangent bundle of an almost parahermitian manifold and study its integrability. Also, the necessary and sufficient conditions are provided for these structures to become para-hyper-Kähler.Key words: para-hyperhermitian structure, tangent bundle, paracomplex space form. PRELIMINARIESAn almost product structure on a smooth manifold M is a tensor field P of type (1,1) on M, P = ±Id, such thatwhere Id is the identity tensor field of type (1,1) on M.An almost para-hermitian structure on a differentiable manifold M is a pair (P, g), where P is an almost product structure on M and g is a semi-Riemannian metric on M satisfyingIn this case, (M, P, g) is said to be an almost para-hermitian manifold. It is easy to see that the dimension of M is even. Moreover, if ∇P = 0, then (M, P, g) is said to be a para-Kähler manifold.An almost complex structure on a smooth manifold M is a tensor field J of type (1,1) on M such thatAn almost para-hypercomplex structure on a smooth manifold M is a triple H = (J α ) α=1,3 , where J 1 is an almost complex structure on M and J 2 , J 3 are almost product structures on M, satisfyingIn this case (M, H) is said to be an almost para-hypercomplex manifold.A semi-Riemannian metric g on (M, H) is said to be compatible or adapted to the almost parahypercomplex structure H = (J α ) α=1,3 if it satisfies Remark 2.3. If (M, P, g) is an almost para-hermitian manifold, then we can define three tensor fields J 1 , J 2 , J 3 on T M by the equalities:It is easy to see that J 1 is an almost complex structure and J 2 , J 3 are almost product structures. We also have the following result (see [15]).

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Section: Is An Almost Para-hypercomplex Structure On T M Which Is Parmentioning

confidence: 99%

Para-hyperhermitian structures on tangent bundles

Vîlcu¹

2011

Proc. Estonian Acad. Sci.

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“…Since the Sasaki metric is rather rigid, several extensions of the Sasaki metric were constructed on T M . We recall here only some, including those obtained by Abbassi and Sarih in [1,2], Janyska [10], Kowalski and Sekizawa [11], Oproiu and Papaghiuc [13], Bejan and Druta-Romaniuc [5].…”

Section: Introductionmentioning

confidence: 99%

Gradient Weyl-Ricci Soliton

Bejan¹,

Meri̇ç²,

Kılıç³

2020

Turk J Math

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“…Sasaki introduced in [14] his well-known Riemannian metric on T M to study some geometric properties of T M endowed with the Sasaki metric. Some extensions of the Sasaki metric were constructed on T M by Abbassi and Sarih [1,2], Janyska [8], Kowalski and Sekizawa [10], Oproiu and Papaghiuc [13], Munteanu [11], Bejan and Druta-Romaniuc [4].…”

Section: Introductionmentioning

confidence: 99%