A non-existence result for compact Einstein warped products

Mustafa, M. T.

doi:10.1088/0305-4470/38/47/l01

Cited by 13 publications

(7 citation statements)

References 6 publications

(7 reference statements)

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“…This completes the proof. Some results concerning Einstein warped products were shown in [15] and [18]. Notice that in our case the Einstein warped product C × f N 2n is noncompact.…”

Section: Harmonic Curvature Tensorsmentioning

confidence: 60%

On a type of almost Kenmotsu manifolds with harmonic curvature tensors

Wang¹,

Liu²

2015

Bull. Belg. Math. Soc. Simon Stevin

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Let M 2n+1 be an almost Kenmotsu manifold with the characteristic vector field belonging to the (k, µ) ′ -nullity distribution. We prove that the curvature tensor of M 2n+1 is harmonic if and only if M 2n+1 is locally isometric to either a product space H n+1 (−4) × R n , or an Einstein warped product C × f N 2n of an open interval and a Ricci-flat almost Kähler manifold. IntroductionA tensor field of type (1, 3) is called an algebraic curvature tensor field if it has symmetric properties of the curvature tensor field of a Riemannian manifold (M, g). It is well known [17] that an algebraic curvature tensor field R on a Riemannian manifold (M, g) is said to be harmonic if (divR)(X, Y, Z) = 0 for any vector fields X, Y, Z on M, where div denotes the divergence operator with respect to the metric g. Following [16], an algebraic curvature tensor field satisfying the second Bianchi identity is harmonic if and only if the associated Ricci operator is of Codazzi type, that is,

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“…This completes the proof. Some results concerning Einstein warped products were shown in [15] and [18]. Notice that in our case the Einstein warped product C × f N 2n is noncompact.…”

Section: Harmonic Curvature Tensorsmentioning

confidence: 60%

On a type of almost Kenmotsu manifolds with harmonic curvature tensors

Wang¹,

Liu²

2015

Bull. Belg. Math. Soc. Simon Stevin

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“…In 2003, Kim and Kim [17] gave the partial answer of Besse question and showed that there does not exist an Einstein warped product space with nonconstant warping function if the scalar curvature is non-positive and base is compact. In 2005, Mustafa [22] generalized the result of Kim and Kim [17] and proved the same result with no condition on scalar curvature.…”

Section: Introductionmentioning

confidence: 64%

“…The purpose of this paper is to extend the result of [16,17,22]. The non-existence of connected compact Einstein doubly warped product semi-Riemannian manifold with nonconstant warping function is proved if the scalar curvature is non-positive.…”

Section: Introductionmentioning

confidence: 80%

On compact Einstein doubly warped product manifolds

Gupta¹

2018

Tamkang J. Math.

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“…He prove that an Einstein warped product space with compact base and nonpositive scalar curvature is just Riemannian product. In 2005, Mustafa [17] construct a result for Einstein warped space with no condition on scalar curvature that is the extension of the theorem in [4]. In [18], D. Dumitru gave some obstructions to the existence of compact Einstein warped products.…”

Section: Relativitymentioning

confidence: 99%

Study on Einstein Warped Product space with Quarter Symmetric Connection

Pal¹,

Kumar²

2022

Preprint

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We study Einstein warped space with a quarter symmetric connection. As a result, first, we find basic results on curvature, Ricci and scalar tensors with respect to the quarter symmetric connection. Moreover, we prove some results corresponding to second order quarter symmetric connection. Finally, we prove that if M is an Einstein warped space with nonpositive scalar curvature and compact base with respect to quarter symmetric connection and the warping function satisfy some condition then M is simply a Riemannian product space.

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A non-existence result for compact Einstein warped products

Cited by 13 publications

References 6 publications

On a type of almost Kenmotsu manifolds with harmonic curvature tensors

On a type of almost Kenmotsu manifolds with harmonic curvature tensors

On compact Einstein doubly warped product manifolds

Study on Einstein Warped Product space with Quarter Symmetric Connection

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