On curvature properties of certain quasi-Einstein hypersurfaces

Ryszard Deszcz; Marian Hotlo; Zerrin EntÜrk

doi:10.1142/S0129167X12500735

On curvature properties of certain quasi-Einstein hypersurfaces

Ryszard Deszcz^*
, Marian Hotlo
, Zerrin EntÜrk

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Wroclaw University of Environmental and Life Sciences
Wrocław University of Science and Technology

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

19 Atıf (Scopus)

Özet

It is known that the Cartan hypersurfaces of dimension 6, 12 or 24 are non-quasi-Einstein, non-pseudosymmetric, Ricci-pseudosymmetric manifolds. In this paper we investigate quasi-Einstein hypersurfaces in semi-Riemannian space forms satisfying some Walker type identity. Among other things we prove that such hypersurfaces are Ricci-pseudosymmetric manifolds. Using certain result of Magid we construct an example of a quasi-Einstein non-pseudosymmetric Ricci-pseudosymmetric warped product which locally can be realized as a hypersurface in a semi-Riemannian space of constant curvature. In our opinion it is a first example of a hypersurface having the mentioned properties.

Orijinal dil	İngilizce
Makale numarası	1250073
Dergi	International Journal of Mathematics
Hacim	23
Basın numarası	7
DOI'lar	https://doi.org/10.1142/S0129167X12500735
Yayın durumu	Yayınlandı - Tem 2012

Finansman

The first two named authors were supported by the grant 2 P03A 006 17 from the Polish State Committee of Scientific Research (KBN). The first named author was also supported by a grant of the Technische Universität Berlin (Germany).

Finansörler
KBN
Polish State Committee of Scientific Research
Technische Universität Berlin

Belgeye Erişim

10.1142/S0129167X12500735

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "On curvature properties of certain quasi-Einstein hypersurfaces",

abstract = "It is known that the Cartan hypersurfaces of dimension 6, 12 or 24 are non-quasi-Einstein, non-pseudosymmetric, Ricci-pseudosymmetric manifolds. In this paper we investigate quasi-Einstein hypersurfaces in semi-Riemannian space forms satisfying some Walker type identity. Among other things we prove that such hypersurfaces are Ricci-pseudosymmetric manifolds. Using certain result of Magid we construct an example of a quasi-Einstein non-pseudosymmetric Ricci-pseudosymmetric warped product which locally can be realized as a hypersurface in a semi-Riemannian space of constant curvature. In our opinion it is a first example of a hypersurface having the mentioned properties.",

keywords = "QuasiEinstein manifold, Ricci-pseudosymmetric hypersurface, Walker type identity, pseudosymmetric hypersurface, pseudosymmetry type manifold, quasi-Einstein hypersurface, warped product",

author = "Ryszard Deszcz and Marian Hotlo and Zerrin Ent{\"U}rk",

year = "2012",

month = jul,

doi = "10.1142/S0129167X12500735",

language = "English",

volume = "23",

journal = "International Journal of Mathematics",

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TY - JOUR

T1 - On curvature properties of certain quasi-Einstein hypersurfaces

AU - Deszcz, Ryszard

AU - Hotlo, Marian

AU - EntÜrk, Zerrin

PY - 2012/7

Y1 - 2012/7

N2 - It is known that the Cartan hypersurfaces of dimension 6, 12 or 24 are non-quasi-Einstein, non-pseudosymmetric, Ricci-pseudosymmetric manifolds. In this paper we investigate quasi-Einstein hypersurfaces in semi-Riemannian space forms satisfying some Walker type identity. Among other things we prove that such hypersurfaces are Ricci-pseudosymmetric manifolds. Using certain result of Magid we construct an example of a quasi-Einstein non-pseudosymmetric Ricci-pseudosymmetric warped product which locally can be realized as a hypersurface in a semi-Riemannian space of constant curvature. In our opinion it is a first example of a hypersurface having the mentioned properties.

AB - It is known that the Cartan hypersurfaces of dimension 6, 12 or 24 are non-quasi-Einstein, non-pseudosymmetric, Ricci-pseudosymmetric manifolds. In this paper we investigate quasi-Einstein hypersurfaces in semi-Riemannian space forms satisfying some Walker type identity. Among other things we prove that such hypersurfaces are Ricci-pseudosymmetric manifolds. Using certain result of Magid we construct an example of a quasi-Einstein non-pseudosymmetric Ricci-pseudosymmetric warped product which locally can be realized as a hypersurface in a semi-Riemannian space of constant curvature. In our opinion it is a first example of a hypersurface having the mentioned properties.

KW - QuasiEinstein manifold

KW - Ricci-pseudosymmetric hypersurface

KW - Walker type identity

KW - pseudosymmetric hypersurface

KW - pseudosymmetry type manifold

KW - quasi-Einstein hypersurface

KW - warped product

UR - https://www.scopus.com/pages/publications/84862996276

U2 - 10.1142/S0129167X12500735

DO - 10.1142/S0129167X12500735

M3 - Article

AN - SCOPUS:84862996276

SN - 0129-167X

VL - 23

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 7

M1 - 1250073

ER -

On curvature properties of certain quasi-Einstein hypersurfaces

Özet

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap