On a certain application of Patterson's curvature identity

Ryszard Deszcz; Marian Hotloś; Zerrin Sentürk

doi:10.5486/pmd.2001.2256

On a certain application of Patterson's curvature identity

Ryszard Deszcz^*, Marian Hotloś, Zerrin Sentürk

^*Corresponding author for this work

Department of Mathematics Engineering

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

3 Citations (Scopus)

Abstract

We present curvature properties of four-dimensional semi-Riemannian manifolds satisfying some condition of pseudosymmetry type. We prove that every such manifold with non-zero associated function L is pseudosymmetric, its scalar curvature does not vanish and L must be equal to 1/3. We also describe non-trivial example of a manifold realizing all these coditions.

Original language	English
Pages (from-to)	93-107
Number of pages	15
Journal	Publicationes Mathematicae Debrecen
Volume	58
Issue number	1
DOIs	https://doi.org/10.5486/pmd.2001.2256
Publication status	Published - 2001

Keywords

Pseudosymmetric manifolds
Semisymmetric manifolds
Weyl conformal curvature tensor

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10.5486/pmd.2001.2256

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abstract = "We present curvature properties of four-dimensional semi-Riemannian manifolds satisfying some condition of pseudosymmetry type. We prove that every such manifold with non-zero associated function L is pseudosymmetric, its scalar curvature does not vanish and L must be equal to 1/3. We also describe non-trivial example of a manifold realizing all these coditions.",

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T1 - On a certain application of Patterson's curvature identity

AU - Deszcz, Ryszard

AU - Hotloś, Marian

AU - Sentürk, Zerrin

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N2 - We present curvature properties of four-dimensional semi-Riemannian manifolds satisfying some condition of pseudosymmetry type. We prove that every such manifold with non-zero associated function L is pseudosymmetric, its scalar curvature does not vanish and L must be equal to 1/3. We also describe non-trivial example of a manifold realizing all these coditions.

AB - We present curvature properties of four-dimensional semi-Riemannian manifolds satisfying some condition of pseudosymmetry type. We prove that every such manifold with non-zero associated function L is pseudosymmetric, its scalar curvature does not vanish and L must be equal to 1/3. We also describe non-trivial example of a manifold realizing all these coditions.

KW - Pseudosymmetric manifolds

KW - Semisymmetric manifolds

KW - Weyl conformal curvature tensor

UR - https://www.scopus.com/pages/publications/0041030284

U2 - 10.5486/pmd.2001.2256

DO - 10.5486/pmd.2001.2256

M3 - Article

AN - SCOPUS:0041030284

SN - 0033-3883

VL - 58

SP - 93

EP - 107

JO - Publicationes Mathematicae Debrecen

JF - Publicationes Mathematicae Debrecen

IS - 1

ER -

On a certain application of Patterson's curvature identity

Abstract

Keywords

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