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Conformal Vector Fields and Null Hypersurfaces
Results in Mathematics, 2022 Abstract We give conditions for a conformal vector field to be tangent to a null hypersurface. We particularize to two important cases: a Killing vector field and a closed and conformal vector field. In the first case, we obtain a result ensuring that a null hypersurface is a Killing horizon.
Benjamin Olea, Olea Benjamin
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Axioms, 2023 A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as an almost-contact B-metric manifold), which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric ...
Mancho Manev
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Local dynamics of conformal vector fields [PDF]
Geometriae Dedicata, 2011 The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian case. This is done using geometric methods, and studying local dynamics of sequences of conformal transformations.
Charles Frances
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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 +3 more
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Closed conformal vector fields on pseudo-Riemannian manifolds [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We give here a geometric proof of the existence of certain local coordinates on a pseudo-Riemannian manifold admitting a closed conformal vector field.
D. A. Catalano
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Navigation problem and conformal vector fields [PDF]
AUT Journal of Mathematics and Computing, 2021 The navigation technique is very effective to obtain or classify a Finsler metric from a given a Finsler metric (especially a Riemannian metric) under an action of a vector field on a differential manifold.
Qiaoling Xia
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2-Conformal Vector Fields on the Model Sol Space and Hyperbolic Ricci Solitons
Journal of MathematicsIn this study, we present the notion of 2-conformal vector fields on Riemannian and semi-Riemannian manifolds, which are an extension of Killing and conformal vector fields. Next, we provide suitable vector fields in Sol space that are 2-conformal. A few
Rawan Bossly +2 more
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Karpatsʹkì Matematičnì Publìkacìï, 2023 The goal of this paper is to find some important Einstein manifolds using conformal Ricci solitons and conformal Ricci almost solitons. We prove that a Kenmotsu metric as a conformal Ricci soliton is Einstein if it is an $\eta$-Einstein or the potential ...
S. Dey
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Bi-conformal vector fields and their applications [PDF]
Classical and Quantum Gravity, 2004 Replaced version with some changes in the terminology and a new theorem.
García-Parrado, Alfonso +1 more
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Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry
Open Mathematics, 2022 We prove that if an η\eta -Einstein para-Kenmotsu manifold admits a conformal η\eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η\eta -Ricci soliton is Einstein if its potential vector field VV is ...
Li Yanlin +3 more
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