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

Symmetry ◽  
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.

scholarly journals Conformal vector fields and Yamabe solitons

2019 ◽  
Vol 16 (04) ◽  
pp. 1950053
Author(s):  
Nasser Bin Turki ◽  
Bang-Yen Chen ◽  
Sharief Deshmukh
Keyword(s):  
Scalar Curvature ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Constant Scalar Curvature ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Yamabe Solitons

In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar curvature. More precisely, we use properties of conformal vector fields to find several sufficient conditions on the soliton vector fields of Yamabe solitons under which their metrics are Yamabe metrics.

Conformal vector fields on Finsler manifolds

2020 ◽  
Vol 31 (12) ◽  
pp. 2050095
Author(s):  
Qiaoling Xia
Keyword(s):  
Sectional Curvature ◽  
Vector Fields ◽  
Riemannian Metric ◽  
Finsler Manifolds ◽  
Conformal Vector ◽  
Conformal Fields ◽  
Special Cases ◽  
Conformal Vector Fields ◽  
Equivalent Characterization

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].

scholarly journals Conformal Vector Fields on Doubly Warped Product Manifolds and Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
H. K. El-Sayied ◽  
Sameh Shenawy ◽  
Noha Syied
Keyword(s):  
Warped Product ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Ricci Solitons ◽  
Ricci Collineations ◽  
Conformal Vector ◽  
Conformal Vector Fields

This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.

Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

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

SINGULAR FOLIATION GENERATED BY AN ORBIT OF FAMILY OF VECTOR FIELDS

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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