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A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold

100%

Papaghiuc N.

Colloquium Mathematicum

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2001

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tom 87

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nr 2

227-233

EN

We consider a certain pseudo-Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).

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An anti-Kählerian Einstein structure on the tangent bundle of a space form

63%

Oproiu V., Papaghiuc N.

Colloquium Mathematicum

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2005

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tom 103

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nr 1

41-46

EN

In [11] we have considered a family of almost anti-Hermitian structures (G,J) on the tangent bundle TM of a Riemannian manifold (M,g), where the almost complex structure J is a natural lift of g to TM interchanging the vertical and horizontal distributions VTM and HTM and the metric G is a natural lift of g of Sasaki type, with the property of being anti-Hermitian with respect to J. Next, we have studied the conditions under which (TM,G,J) belongs to one of the eight classes of anti-Hermitian structures obtained in the classification in [2]. In this paper, we study some geometric properties of the anti-Kählerian structure obtained in [11]. In fact we prove that it is Einstein. This result offers nice examples of anti-Kählerian Einstein manifolds studied in [1].

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Semi-invariant submanifolds of a Sasakian space form

38%

Bejancu A., Papaghiuc N.

Colloquium Mathematicum

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1984

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tom 48

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nr 2

229-240

Ograniczanie wyników

3 Colloquium Mathematicum

3 Papaghiuc N.

1 Bejancu A.

1 Oproiu V.

1 2005

1 2001

1 1984

A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold

An anti-Kählerian Einstein structure on the tangent bundle of a space form

Semi-invariant submanifolds of a Sasakian space form