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Geometry of Conformal Vector Fields

Arab Journal of Mathematical Sciences, 2017
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Sharief Deshmukh
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On m-Modified Conformal Vector Fields

Journal of Geometric Analysis, 2023
The authors introduce the notion of \(m\)-modified conformal vector fields. It is shown that compact Riemannian manifolds admit no \(m\)-modified conformal vector fields of constant length. It is also shown that the existence of a left-invariant \(m\)-modified conformal vector field on a Riemannian Lie group \(\left( G,\left\langle \cdot ,\cdot \right ...
Zhang, Hui, Chen, Zhiqi
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Conformal Vector Fields on Spacetimes

Annals of Global Analysis and Geometry, 2006
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Conformal vector fields and σk-scalar curvatures

Pacific Journal of Mathematics, 2022
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Xu, Xingwang, Ye, Jian
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Zeros of conformal vector fields

Classical and Quantum Gravity, 1997
The authors study the behaviour of a conformal vector field \(X\) on a spacetime in the neighbourhood of a zero of \(X\).
Hall, G. S., Capocci, M. S., Beig, R.
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Conformal Vector Fields on Some Finsler Manifolds [PDF]

Science China Mathematics, 2016
We study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields.
Mingao Yuan
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Conformal Vector Fields and Totally Umbilic Hypersurfaces [PDF]

Bulletin of the Korean Mathematical Society, 2002
Let \((M^n,g)\), \(n\geq 2\), be a connected semi-Riemannian hypersurface of a semi-Riemannian space form \((\overline{M}_k^{n+1}(\overline{c}),\overline{g})\) of signature \(k\). Assume that the ambient manifold carries a conformal vector field \(V\) such that the tangential part \((V|M^n)^T\) becomes a conformal vector field on the hypersurface. Then
Kim, Dong-Soo, Kim, Seon-Bu, Kim, Young Ho, Park, Seong-Hee   +3 more
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On Conformal Vector Fields on Randers Manifolds

Science China Mathematics, 2012
In an \(n\)-dimensional Finsler manifold \((M,F)\), a diffeomorphism \(\varphi\) is called a conformal transformation if it satisfies \(F(\varphi(x),\varphi_\ast(y))= e^{2c(x)}F(x,y)\), where \(y\in T_xM\), \(c(x)\) is a function on \(M\) and \(\varphi_\ast:T_xM\longrightarrow T_{\varphi(x)}M\) is the tangent map at a point \(x\).
Qiaoling Xia
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On $\phi$-skew symmetric conformal vector fields

Publicationes Mathematicae Debrecen, 2001
Summary: The notion of the \(J\)-skew symmetric vector field was introduced by \textit{I. Mihai, L. Nicolescu} and \textit{R. Rosca} [Port. Math. 54, 215-228 (1997; Zbl 0880.53029)]. In the present paper, we deal with \(\varphi\)-skew symmetric conformal vector fields on a Kenmotsu manifold \(M(\varphi,\Omega,\eta,\xi,g)\).
Naitza, Dorotea, Oiagă, Adela
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Conformal Vector Fields on Kaehler Manifolds

Annali Dell'Universita Di Ferrara, 2011
The author studies analytic conformal vector fields on non-compact Kähler manifolds \(M\) and looks for necessary conditions in order that such objects become Killing vector fields. The main results of the paper prove that two such additional hypothesis are: (i) \(\dim M \neq 4\) ; \(M\) has constant nowhere vanishing scalar curvature.
Sharief Deshmukh
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