Conformal vector fields on Finsler manifolds

In this paper, we give an equivalent characterization of conformal vector fields on a Finsler manifold [Formula: see text], whose metric [Formula: see text] is defined by a Riemannian metric [Formula: see text] and a 1-form [Formula: see text]. This characterization contains all related results in [Z. Shen and Q. Xia, On conformal vector fields on Randers manifolds, Sci. China Math. 55(9) (2012) 1869–1882; Z. Shen and M. Yuan, Conformal vector fields on some Finsler manifolds, Sci. China Math. 59(1) (2016) 107–114; X. Cheng, Y. Li and T. Li, The conformal vector fields on Kropina manifolds, Diff. Geom. Appl. 56 (2018) 344–354] as special cases. Further, we determine conformal fields on some Finsler manifolds [Formula: see text] when [Formula: see text] is of constant sectional curvature and [Formula: see text] is a conformal 1-form with respect to [Formula: see text].

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Bi-conformal vector fields and the local geometric characterization of conformally separable pseudo-Riemannian manifolds I

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2005.06.005 ◽

2006 ◽

Vol 56 (7) ◽

pp. 1069-1095 ◽

Cited By ~ 7

Author(s):

Alfonso García-Parrado Gómez-Lobo

Keyword(s):

Riemannian Manifolds ◽

Vector Fields ◽

Geometric Characterization ◽

Conformal Vector ◽

Conformal Vector Fields

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Bi-conformal vector fields and the local geometric characterization of conformally separable pseudo-Riemannian manifolds II

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2005.08.005 ◽

2006 ◽

Vol 56 (9) ◽

pp. 1600-1622 ◽

Cited By ~ 1

Author(s):

Alfonso García-Parrado Gómez-Lobo

Keyword(s):

Riemannian Manifolds ◽

Vector Fields ◽

Geometric Characterization ◽

Conformal Vector ◽

Conformal Vector Fields

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Conformal vector fields on some Finsler manifolds

Science China Mathematics ◽

10.1007/s11425-015-5099-9 ◽

2015 ◽

Vol 59 (1) ◽

pp. 107-114 ◽

Cited By ~ 5

Author(s):

ZhongMin Shen ◽

MinGao Yuan

Keyword(s):

Vector Fields ◽

Finsler Manifolds ◽

Conformal Vector ◽

Conformal Vector Fields

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Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

Symmetry ◽

10.3390/sym13122362 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2362

Author(s):

Ali H. Alkhaldi ◽

Pişcoran Laurian-Ioan ◽

Abimbola Abolarinwa ◽

Akram Ali

Keyword(s):

Scalar Curvature ◽

Vector Fields ◽

Sufficient Conditions ◽

Constant Scalar Curvature ◽

Topological Constraints ◽

Conformal Vector ◽

Conformal Vector Fields ◽

Yamabe Solitons

In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics.

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Conformal Vector Fields on Finsler Space with Special (α , β )- Metric

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2019/v31i430117 ◽

2019 ◽

pp. 1-8

Author(s):

N. Natesh ◽

S. K. Narasimhamurthy ◽

M. K. Roopa

Keyword(s):

Vector Fields ◽

Finsler Space ◽

Riemannian Metric ◽

Finsler Metrics ◽

Conformal Vector ◽

Conformal Vector Fields ◽

Beta 2

In this paper, we study the conformal vector elds on a class of Finsler metrics. In particular Finsler space with special (α, β)- metric `F =\alpha +\frac{\beta^2}{\alpha} ` is dened in Riemannian metric α and 1-form β and its norm. Then we characterize the PDE's of conformal vector elds on Finsler space with special (α, β)- metric.

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Lie groups with conformal vector fields induced by derivations

Journal of Algebra ◽

10.1016/j.jalgebra.2021.05.020 ◽

2021 ◽

Author(s):

Hui Zhang ◽

Zhiqi Chen

Keyword(s):

Lie Groups ◽

Vector Fields ◽

Conformal Vector ◽

Conformal Vector Fields

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Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

Mediterranean Journal of Mathematics ◽

10.1007/s00009-020-01690-5 ◽

2021 ◽

Vol 18 (2) ◽

Author(s):

Mohamed Tahar Kadaoui Abbassi ◽

Noura Amri ◽

Cornelia-Livia Bejan

Keyword(s):

Vector Fields ◽

Ricci Soliton ◽

Conformal Vector ◽

Conformal Vector Fields

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SINGULAR FOLIATION GENERATED BY AN ORBIT OF FAMILY OF VECTOR FIELDS

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.4.28 ◽

2021 ◽

Vol 10 (4) ◽

pp. 2141-2147

Author(s):

X.F. Sharipov ◽

B. Boymatov ◽

N. Abriyev

Keyword(s):

Dynamical Systems ◽

Euclidean Space ◽

Control Theory ◽

Vector Fields ◽

Singular Foliation ◽

Completely Integrable ◽

Conformal Vector ◽

Conformal Vector Fields ◽

Systems Control

Geometry of orbit is a subject of many investigations because it has important role in many branches of mathematics such as dynamical systems, control theory. In this paper it is studied geometry of orbits of conformal vector fields. It is shown that orbits of conformal vector fields are integral submanifolds of completely integrable distributions. Also for Euclidean space it is proven that if all orbits have the same dimension they are closed subsets.

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