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
收藏
页数：16
相关论文
共 50 条
  • [1] A NOTE ON *-CONFORMAL AND GRADIENT *-CONFORMAL η-RICCI SOLITONS IN α-COSYMPLECTIC MANIFOLDS
    Haseeb, Abdul
    Prasad, Rajendra
    Chaubey, Sudhakar K.
    Vanli, Aysel Turgut
    [J]. HONAM MATHEMATICAL JOURNAL, 2022, 44 (02): : 231 - 243
  • [2] Conformal Diffeomorphisms of Gradient Ricci Solitons and Generalized Quasi-Einstein Manifolds
    Jeffrey L. Jauregui
    William Wylie
    [J]. The Journal of Geometric Analysis, 2015, 25 : 668 - 708
  • [3] Conformal Diffeomorphisms of Gradient Ricci Solitons and Generalized Quasi-Einstein Manifolds
    Jauregui, Jeffrey L.
    Wylie, William
    [J]. JOURNAL OF GEOMETRIC ANALYSIS, 2015, 25 (01) : 668 - 708
  • [4] Einstein manifolds and conformal field theories
    Gubser, SS
    [J]. PHYSICAL REVIEW D, 1999, 59 (02)
  • [5] Quasi-Einstein manifolds admitting a closed conformal vector field
    Silva Filho, J. F.
    [J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2024, 92
  • [6] On homogeneous η-Einstein almost cosymplectic manifolds
    Lotta, Antonio
    [J]. BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, 2024, 65 (03): : 745 - 749
  • [7] Gradient Einstein solitons
    Catino, Giovanni
    Mazzieri, Lorenzo
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 132 : 66 - 94
  • [8] Einstein–Weyl structures on almost cosymplectic manifolds
    Xiaomin Chen
    [J]. Periodica Mathematica Hungarica, 2019, 79 : 191 - 203
  • [9] Gradient ρ-Einstein solitons on almost Co-Kahler manifolds
    Biswas, Gour Gopal
    De, Uday Chand
    [J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2023, 20 (06)
  • [10] Generalized m-Quasi-Einstein manifolds admitting a closed conformal vector field
    Rahul Poddar
    S. Balasubramanian
    Ramesh Sharma
    [J]. Annali di Matematica Pura ed Applicata (1923 -), 2023, 202 : 2687 - 2697
12345