On some family of generalized Einstein metric conditions

Ryszard Deszcz; Marian Hotloś; Zerrin Sentürk

doi:10.1515/dema-2001-0422

On some family of generalized Einstein metric conditions

Ryszard Deszcz, Marian Hotloś, Zerrin Sentürk

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We prove that every Einstein manifold of dimension > 4 satisfies some pseudosymmetry type curvature condition. Basing on this fact we introduce a family of curvature conditions. We investigate non-Einstein manifolds satisfying one of these conditions. We prove that every such manifold is pseudosymmetric and satisfies other curvature conditions. We prove also an inverse theorem.

Original language	English
Pages (from-to)	943-954
Number of pages	12
Journal	Demonstratio Mathematica
Volume	34
Issue number	4
DOIs	https://doi.org/10.1515/dema-2001-0422
Publication status	Published - Oct 2001

Bibliographical note

Publisher Copyright:
© 2001 Warsaw University. All rights reserved.

Keywords

Einstein manifold
Generalized Einstein metric condition.
Pseudosymmetry type manifold

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10.1515/dema-2001-0422

Cite this

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abstract = "We prove that every Einstein manifold of dimension > 4 satisfies some pseudosymmetry type curvature condition. Basing on this fact we introduce a family of curvature conditions. We investigate non-Einstein manifolds satisfying one of these conditions. We prove that every such manifold is pseudosymmetric and satisfies other curvature conditions. We prove also an inverse theorem.",

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AU - Hotloś, Marian

AU - Sentürk, Zerrin

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AB - We prove that every Einstein manifold of dimension > 4 satisfies some pseudosymmetry type curvature condition. Basing on this fact we introduce a family of curvature conditions. We investigate non-Einstein manifolds satisfying one of these conditions. We prove that every such manifold is pseudosymmetric and satisfies other curvature conditions. We prove also an inverse theorem.

KW - Einstein manifold

KW - Generalized Einstein metric condition.

KW - Pseudosymmetry type manifold

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DO - 10.1515/dema-2001-0422

M3 - Article

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SN - 0420-1213

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EP - 954

JO - Demonstratio Mathematica

JF - Demonstratio Mathematica

IS - 4

ER -

On some family of generalized Einstein metric conditions

Abstract

Bibliographical note

Keywords

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