Conformal vector field and gradient Einstein solitons on ?-Einstein cosymplectic manifolds

被引：0

作者：

Chaubey, Sudhakar Kumar ^{[1
]}

De, Uday Chand ^{[2
]}

Suh, Young Jin ^{[3
,4
]}

机构：

[1] Univ Technol & Appl Sci, Dept Informat Technol, Sect Math, POB 77, Shinas 324, Oman

[2] Univ Calcutta, Dept Pure Math, 35 Ballygaunge Circular Rd, Kolkata 700019, West Bengal, India

[3] Kyungpook Natl Univ, Dept Math, Daegu 41566, South Korea

[4] Kyungpook Natl Univ, RIRCM, Daegu 41566, South Korea

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2023年 / 20卷 / 08期

基金：

新加坡国家研究基金会;

关键词：

Cosymplectic manifolds; gradient Einstein soliton; conformal vector field; homothetic vector field; RICCI SOLITONS; CLASSIFICATION;

D O I：

10.1142/S0219887823501359

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we characterize the ?-Einstein cosymplectic manifolds with the gradient Einstein solitons and the conformal vector fields. It is proven that if an ?-Einstein cosymplectic manifold M2n+1 of dimension 2n + 1 with n > 1 admits a gradient Einstein soliton, then either M2n+1 is Ricci flat or the gradient of Einstein potential function is pointwise collinear with the Reeb vector field of M2n+1. Also, we prove that if M2n+1 admits a conformal vector field W, then either M2n+1 is Ricci flat or W is homothetic. We also establish that a conformal vector field W on M2n+1 is a strict infinitesimal contact transformation, provided the scalar curvature of M2n+1 is constant. Finally, the non-trivial examples of cosymplectic manifolds admitting the gradient Einstein solitons are given.

引用

页数：16

共 50 条

[21] Gradient Yamabe and Gradient m-Quasi Einstein Metrics on Three-dimensional Cosymplectic Manifolds
Uday Chand De
Sudhakar K. Chaubey
Young Jin Suh
[J]. Mediterranean Journal of Mathematics, 2021, 18
[22] Quasi-Einstein structures and almost cosymplectic manifolds
Chen, Xiaomin
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2020, 114 (02)
[23] Quasi-Einstein structures and almost cosymplectic manifolds
Xiaomin Chen
[J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, 114
[24] Einstein solitons with unit geodesic potential vector field
Blaga, Adara M.
Deshmukh, Sharief
[J]. AIMS MATHEMATICS, 2021, 6 (08): : 7961 - 7970
[25] Einstein-Weyl structures on almost cosymplectic manifolds
Chen, Xiaomin
[J]. PERIODICA MATHEMATICA HUNGARICA, 2019, 79 (02) : 191 - 203
[26] Geometry of gradient Einstein harmonic solitons in sequential warped products manifolds
Ali, Akram
Alshehri, Norah
Mofarreh, Fatemah
Li, Yanlin
[J]. EUROPEAN PHYSICAL JOURNAL PLUS, 2024, 139 (04):
[27] Remarks on Einstein Solitons with Certain Types of Vector Field
Blaga, Adara M.
Latcu, Dan Radu
[J]. INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2021, 14 (01): : 100 - 105
[28] Ricci Solitons on η-Einstein Contact Manifolds
Chand, De Uday
Suh, Young Jin
Majhi, Pradip Kumar
[J]. FILOMAT, 2018, 32 (13) : 4679 - 4687
[29] GRADIENT VECTOR-FIELDS ON COSYMPLECTIC MANIFOLDS
CANTRIJN, F
DELEON, M
LACOMBA, EA
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992, 25 (01): : 175 - 188
[30] Conformal vector fields on f-cosymplectic manifolds
Sardar, Arpan
De, Uday Chand
Suh, Young Jin
[J]. FILOMAT, 2023, 37 (17) : 5649 - 5658

← 1 2 3 4 5 →