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

11 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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T1 - On some family of generalized Einstein metric conditions

AU - Deszcz, Ryszard

AU - Hotloś, Marian

AU - Sentürk, Zerrin

PY - 2001/10

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/84977790718

U2 - 10.1515/dema-2001-0422

DO - 10.1515/dema-2001-0422

M3 - Article

AN - SCOPUS:84977790718

SN - 0420-1213

VL - 34

SP - 943

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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