Sectional curvatures on Weyl manifolds with a special metric connection

Fatma Özdemir; Mustafa Deniz Türkoğlu

doi:10.3906/mat-1803-121

Sectional curvatures on Weyl manifolds with a special metric connection

Fatma Özdemir^*
, Mustafa Deniz Türkoğlu

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Technical University

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

2 Citations (Scopus)

Abstract

In this paper, Weyl manifolds, denoted by WS(g, w, π, μ), having a special a semisymmetric recurrentmetric connection are introduced and the uniqueness of this connection is proved. We give an example of WS(g;w; π, μ) with a constant scalar curvature. Furthermore, we define sectional curvatures of WS(g;w; π, μ) and prove that any isotropic Weyl manifold WS(g;w; π, μ) is locally conformal to an Einstein manifold with a semisymmetric recurrentmetric connection, EWS(g;w; π, μ) .

Original language	English
Pages (from-to)	224-240
Number of pages	17
Journal	Turkish Journal of Mathematics
Volume	43
Issue number	1
DOIs	https://doi.org/10.3906/mat-1803-121
Publication status	Published - 2019

Bibliographical note

Publisher Copyright:
© TÜBI˙TAK.

Keywords

Generalized Bianchi identities
Recurrent-metric connection
Sectional curvature
Semisymmetric connection
Weyl manifold

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10.3906/mat-1803-121

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title = "Sectional curvatures on Weyl manifolds with a special metric connection",

abstract = "In this paper, Weyl manifolds, denoted by WS(g, w, π, μ), having a special a semisymmetric recurrentmetric connection are introduced and the uniqueness of this connection is proved. We give an example of WS(g;w; π, μ) with a constant scalar curvature. Furthermore, we define sectional curvatures of WS(g;w; π, μ) and prove that any isotropic Weyl manifold WS(g;w; π, μ) is locally conformal to an Einstein manifold with a semisymmetric recurrentmetric connection, EWS(g;w; π, μ) .",

keywords = "Generalized Bianchi identities, Recurrent-metric connection, Sectional curvature, Semisymmetric connection, Weyl manifold",

author = "Fatma {\"O}zdemir and T{\"u}rkoğlu, \{Mustafa Deniz\}",

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year = "2019",

doi = "10.3906/mat-1803-121",

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T1 - Sectional curvatures on Weyl manifolds with a special metric connection

AU - Özdemir, Fatma

AU - Türkoğlu, Mustafa Deniz

N1 - Publisher Copyright: © TÜBI˙TAK.

PY - 2019

Y1 - 2019

N2 - In this paper, Weyl manifolds, denoted by WS(g, w, π, μ), having a special a semisymmetric recurrentmetric connection are introduced and the uniqueness of this connection is proved. We give an example of WS(g;w; π, μ) with a constant scalar curvature. Furthermore, we define sectional curvatures of WS(g;w; π, μ) and prove that any isotropic Weyl manifold WS(g;w; π, μ) is locally conformal to an Einstein manifold with a semisymmetric recurrentmetric connection, EWS(g;w; π, μ) .

AB - In this paper, Weyl manifolds, denoted by WS(g, w, π, μ), having a special a semisymmetric recurrentmetric connection are introduced and the uniqueness of this connection is proved. We give an example of WS(g;w; π, μ) with a constant scalar curvature. Furthermore, we define sectional curvatures of WS(g;w; π, μ) and prove that any isotropic Weyl manifold WS(g;w; π, μ) is locally conformal to an Einstein manifold with a semisymmetric recurrentmetric connection, EWS(g;w; π, μ) .

KW - Generalized Bianchi identities

KW - Recurrent-metric connection

KW - Sectional curvature

KW - Semisymmetric connection

KW - Weyl manifold

UR - https://www.scopus.com/pages/publications/85061625177

U2 - 10.3906/mat-1803-121

DO - 10.3906/mat-1803-121

M3 - Article

AN - SCOPUS:85061625177

SN - 1300-0098

VL - 43

SP - 224

EP - 240

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 1

ER -

Sectional curvatures on Weyl manifolds with a special metric connection

Abstract

Bibliographical note

Keywords

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