On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds

Ryszard Deszcz; Małgorzata Głogowska; Marian Hotlos; Zerrin Şentürk

doi:10.1063/5.0118057

On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds

Ryszard Deszcz, Małgorzata Głogowska, Marian Hotlos, Zerrin Şentürk^*

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

The tensor R · C − C · R and the tensors Q(g, R), Q(S, R), Q(g, C) and Q(S, C) of every Einstein manifold (M, g), n ≥ 4, satisfy R · C − C · R = (κ/((n − 1)n)) Q(g, R) = (κ/((n − 1)n)) Q(g, C) = (1/(n − 1)) Q(S, R) = (1/(n − 1)) Q(S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension ≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R· C − C · R is a linear combination of the tensors Q(g, R), Q(S, R), Q(g, C), Q(S, C), Q(g, g ∧ S ) and Q(S, g ∧ S ). We present results on quasi-Einstein and 2-quasi-Einstein warped product manifolds satisfying particular conditions of these family of conditions.

Original language	English
Title of host publication	5th International Conference of Mathematical Sciences, ICMS 2021
Editors	Huseyin Cakalli, Ljubisa D. R. Kocinac, Allaberen Ashyralyev, Robin Harte, Mehmet Dik, Ibrahim Canak, Hacer Sengul Kandemir, Mujgan Tez, Ozay Gurtug, Ekrem Savas, Nazlim Deniz Aral, Filiz Cagatay Ucgan, Onder Sahinaslan, Charyyar Ashyralyyev, Sefa Anil Sezer, Arap Duran Turkoglu, Oruc Raif Onvural, Hakan Sahin
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735442580
DOIs	https://doi.org/10.1063/5.0118057
Publication status	Published - 7 Nov 2022
Event	5th International Conference of Mathematical Sciences, ICMS 2021 - Istanbul, Turkey Duration: 23 Jun 2021 → 27 Jun 2021

Publication series

Name	AIP Conference Proceedings
Volume	2483
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	5th International Conference of Mathematical Sciences, ICMS 2021
Country/Territory	Turkey
City	Istanbul
Period	23/06/21 → 27/06/21

Bibliographical note

Publisher Copyright:
© 2022 American Institute of Physics Inc.. All rights reserved.

Keywords

2-quasi-Einstein manifold
Einstein manifold
generalized Einstein metric condition
pseudosymmetry type curvature condition
quasi-Einstein manifold
warped product manifold

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10.1063/5.0118057

Cite this

Deszcz, R., Głogowska, M., Hotlos, M., & Şentürk, Z. (2022). On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds. In H. Cakalli, L. D. R. Kocinac, A. Ashyralyev, R. Harte, M. Dik, I. Canak, H. S. Kandemir, M. Tez, O. Gurtug, E. Savas, N. D. Aral, F. C. Ucgan, O. Sahinaslan, C. Ashyralyyev, S. A. Sezer, A. D. Turkoglu, O. R. Onvural, & H. Sahin (Eds.), 5th International Conference of Mathematical Sciences, ICMS 2021 Article 100001 (AIP Conference Proceedings; Vol. 2483). American Institute of Physics Inc.. https://doi.org/10.1063/5.0118057

Deszcz, Ryszard ; Głogowska, Małgorzata ; Hotlos, Marian et al. / On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds. 5th International Conference of Mathematical Sciences, ICMS 2021. editor / Huseyin Cakalli ; Ljubisa D. R. Kocinac ; Allaberen Ashyralyev ; Robin Harte ; Mehmet Dik ; Ibrahim Canak ; Hacer Sengul Kandemir ; Mujgan Tez ; Ozay Gurtug ; Ekrem Savas ; Nazlim Deniz Aral ; Filiz Cagatay Ucgan ; Onder Sahinaslan ; Charyyar Ashyralyyev ; Sefa Anil Sezer ; Arap Duran Turkoglu ; Oruc Raif Onvural ; Hakan Sahin. American Institute of Physics Inc., 2022. (AIP Conference Proceedings).

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title = "On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds",

abstract = "The tensor R · C − C · R and the tensors Q(g, R), Q(S, R), Q(g, C) and Q(S, C) of every Einstein manifold (M, g), n ≥ 4, satisfy R · C − C · R = (κ/((n − 1)n)) Q(g, R) = (κ/((n − 1)n)) Q(g, C) = (1/(n − 1)) Q(S, R) = (1/(n − 1)) Q(S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension ≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R· C − C · R is a linear combination of the tensors Q(g, R), Q(S, R), Q(g, C), Q(S, C), Q(g, g ∧ S ) and Q(S, g ∧ S ). We present results on quasi-Einstein and 2-quasi-Einstein warped product manifolds satisfying particular conditions of these family of conditions.",

keywords = "2-quasi-Einstein manifold, Einstein manifold, generalized Einstein metric condition, pseudosymmetry type curvature condition, quasi-Einstein manifold, warped product manifold",

author = "Ryszard Deszcz and Ma{\l}gorzata G{\l}ogowska and Marian Hotlos and Zerrin {\c S}ent{\"u}rk",

note = "Publisher Copyright: {\textcopyright} 2022 American Institute of Physics Inc.. All rights reserved.; 5th International Conference of Mathematical Sciences, ICMS 2021 ; Conference date: 23-06-2021 Through 27-06-2021",

year = "2022",

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doi = "10.1063/5.0118057",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Huseyin Cakalli and Kocinac, {Ljubisa D. R.} and Allaberen Ashyralyev and Robin Harte and Mehmet Dik and Ibrahim Canak and Kandemir, {Hacer Sengul} and Mujgan Tez and Ozay Gurtug and Ekrem Savas and Aral, {Nazlim Deniz} and Ucgan, {Filiz Cagatay} and Onder Sahinaslan and Charyyar Ashyralyyev and Sezer, {Sefa Anil} and Turkoglu, {Arap Duran} and Onvural, {Oruc Raif} and Hakan Sahin",

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Deszcz, R, Głogowska, M, Hotlos, M & Şentürk, Z 2022, On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds. in H Cakalli, LDR Kocinac, A Ashyralyev, R Harte, M Dik, I Canak, HS Kandemir, M Tez, O Gurtug, E Savas, ND Aral, FC Ucgan, O Sahinaslan, C Ashyralyyev, SA Sezer, AD Turkoglu, OR Onvural & H Sahin (eds), 5th International Conference of Mathematical Sciences, ICMS 2021., 100001, AIP Conference Proceedings, vol. 2483, American Institute of Physics Inc., 5th International Conference of Mathematical Sciences, ICMS 2021, Istanbul, Turkey, 23/06/21. https://doi.org/10.1063/5.0118057

On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds. / Deszcz, Ryszard; Głogowska, Małgorzata; Hotlos, Marian et al.
5th International Conference of Mathematical Sciences, ICMS 2021. ed. / Huseyin Cakalli; Ljubisa D. R. Kocinac; Allaberen Ashyralyev; Robin Harte; Mehmet Dik; Ibrahim Canak; Hacer Sengul Kandemir; Mujgan Tez; Ozay Gurtug; Ekrem Savas; Nazlim Deniz Aral; Filiz Cagatay Ucgan; Onder Sahinaslan; Charyyar Ashyralyyev; Sefa Anil Sezer; Arap Duran Turkoglu; Oruc Raif Onvural; Hakan Sahin. American Institute of Physics Inc., 2022. 100001 (AIP Conference Proceedings; Vol. 2483).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds

AU - Deszcz, Ryszard

AU - Głogowska, Małgorzata

AU - Hotlos, Marian

AU - Şentürk, Zerrin

PY - 2022/11/7

Y1 - 2022/11/7

N2 - The tensor R · C − C · R and the tensors Q(g, R), Q(S, R), Q(g, C) and Q(S, C) of every Einstein manifold (M, g), n ≥ 4, satisfy R · C − C · R = (κ/((n − 1)n)) Q(g, R) = (κ/((n − 1)n)) Q(g, C) = (1/(n − 1)) Q(S, R) = (1/(n − 1)) Q(S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension ≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R· C − C · R is a linear combination of the tensors Q(g, R), Q(S, R), Q(g, C), Q(S, C), Q(g, g ∧ S ) and Q(S, g ∧ S ). We present results on quasi-Einstein and 2-quasi-Einstein warped product manifolds satisfying particular conditions of these family of conditions.

AB - The tensor R · C − C · R and the tensors Q(g, R), Q(S, R), Q(g, C) and Q(S, C) of every Einstein manifold (M, g), n ≥ 4, satisfy R · C − C · R = (κ/((n − 1)n)) Q(g, R) = (κ/((n − 1)n)) Q(g, C) = (1/(n − 1)) Q(S, R) = (1/(n − 1)) Q(S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension ≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R· C − C · R is a linear combination of the tensors Q(g, R), Q(S, R), Q(g, C), Q(S, C), Q(g, g ∧ S ) and Q(S, g ∧ S ). We present results on quasi-Einstein and 2-quasi-Einstein warped product manifolds satisfying particular conditions of these family of conditions.

KW - 2-quasi-Einstein manifold

KW - Einstein manifold

KW - generalized Einstein metric condition

KW - pseudosymmetry type curvature condition

KW - quasi-Einstein manifold

KW - warped product manifold

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U2 - 10.1063/5.0118057

DO - 10.1063/5.0118057

M3 - Conference contribution

AN - SCOPUS:85142524063

T3 - AIP Conference Proceedings

BT - 5th International Conference of Mathematical Sciences, ICMS 2021

A2 - Cakalli, Huseyin

A2 - Kocinac, Ljubisa D. R.

A2 - Ashyralyev, Allaberen

A2 - Harte, Robin

A2 - Dik, Mehmet

A2 - Canak, Ibrahim

A2 - Kandemir, Hacer Sengul

A2 - Tez, Mujgan

A2 - Gurtug, Ozay

A2 - Savas, Ekrem

A2 - Aral, Nazlim Deniz

A2 - Ucgan, Filiz Cagatay

A2 - Sahinaslan, Onder

A2 - Ashyralyyev, Charyyar

A2 - Sezer, Sefa Anil

A2 - Turkoglu, Arap Duran

A2 - Onvural, Oruc Raif

A2 - Sahin, Hakan

PB - American Institute of Physics Inc.

T2 - 5th International Conference of Mathematical Sciences, ICMS 2021

Y2 - 23 June 2021 through 27 June 2021

ER -

Deszcz R, Głogowska M, Hotlos M, Şentürk Z. On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds. In Cakalli H, Kocinac LDR, Ashyralyev A, Harte R, Dik M, Canak I, Kandemir HS, Tez M, Gurtug O, Savas E, Aral ND, Ucgan FC, Sahinaslan O, Ashyralyyev C, Sezer SA, Turkoglu AD, Onvural OR, Sahin H, editors, 5th International Conference of Mathematical Sciences, ICMS 2021. American Institute of Physics Inc. 2022. 100001. (AIP Conference Proceedings). doi: 10.1063/5.0118057

On Some Quasi-Einstein and 2-Quasi-Einstein Manifolds

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