arXiv research

The study classifies spaces with specific conformal vector fields.

In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds with nonpositive Ricci curvature, thus generalizing a theorem of T. K. Pan. Then…

The paper proves conditions for compact vacuum static spaces to be isometric to spheres.

The study classifies gradient Ricci solitons with specific vector fields.

The paper examines timelike conformal fields on 3-manifolds and finds they are rigidly tied to specific geometric structures.

Conditions for Riemannian manifolds to be Euclidean spheres or spaces.

The study extends and generalizes a result about quasi Einstein manifolds, proving conditions for Killing vector fields.

Local Lorentzian theorem preserves metrics or makes them flat.

Study the isoperimetric problem in Riemannian manifolds with non-trivial conformal vector fields.

Study foliations on Riemannian manifolds with specific vector fields, focusing on geometric properties.

A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometri…

Conformal vector fields on LCP manifolds are orthogonal and Killing.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

New approach classifies conformal Killing vector fields for FLRW space-time.

Conformal vector fields on lcK manifolds are shown to be Killing or holomorphic.

Study proves conformal vector fields on certain Finsler manifolds are Killing fields.

In this paper, we investigated the behavior of left-invariant conformal vector fields on Lie groups with left-invariant pseudo-Riemannian metrics. First of all, we prove that conformal vector fields on pseudo-Riemannian unimodular Lie groups are Killing. Then we obtain a necessary condition for a pseudo-Rimennian non-u…

In this paper we introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution of this flow, discuss its convergence and possible applications, and its relation to the …

Geodesic vector fields on flat 3-manifolds are related to contact structures.

In this paper, we study locally strongly convex Tchebychev hypersurfaces, namely the {\it centroaffine totally umbilical hypersurfaces}, in the $(n+1)$-dimensional affine space $\mathbb{R}^{n+1}$. We first make an ordinary-looking observation that such hypersurfaces are characterized by having a Riemannian structure ad…

Study null conformal Killing vector fields on complex surfaces.

In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(α,β)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of some classes of $(α,β)$ spaces under certain c…

Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The conformal and fiber preserving vector fields on TM have well-known physical interpretations and have been studied by physicists and geometricians. Here we define a Riemannian or pseudo-Riemannian lift metric on TM, which is in some senses more…

In this paper, we characterize conformal vector fields of any (regular or singular) $(α,β)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(α,β)$-spaces satisfying certain geometric conditions.

In this paper, it is proved that any conformal vector field is homothetic on a locally projectively flat $(α,β)$-space of non-Randers type in dimension $n\ge 3$, and the local solutions of such a vector field are determined. While on a locally projectively flat Randers space, examples showthat the conformal vector fiel…

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …

The paper investigates Ricci almost solitons linked to conformal vector fields.

In this article, we present a complete study of two disjoint classes of conformal vector fields on doubly warped product manifolds as well as on doubly warped space-times. Then we study Ricci solitons on doubly warped product manifollds admitting these types of conformal vector fields.

We show that if a connected compact kählerian surface $M$ with nonpositive gaussian curvature is furnished with a closed conformal vector field $ξ$ whose singular points are isolated, then $M$ is isometric to a flat torus and $ξ$ is parallel. We also consider the case of a connected complete kählerian manifod $M$ of co…

The paper proves non-existence of torqued and anti-torqued vector fields on hyperbolic spaces.

The paper explores properties of conformal vector fields on almost Kenmotsu manifolds.

Let $(M^n,g)$ be an $n$-dimensional compact connected Riemannian manifold with smooth boundary. We show that the presence of a nontrivial conformal gradient vector field on $M$, with an appropriate control on the Ricci curvature makes $M$ to be isometric to a hemisphere of $\mathbb{S}^{n}$. We also prove that if an Ein…

The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for manifold with boundary is used. The identification allows the derivation of gov…

The paper studies conformal Ricci solitons in warped product spaces.

The paper studies special solitons on Riemannian manifolds with specific vector fields.

A vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected non-flat space form other than the 2-sphere, examples are obtained of conformal vecto…

In Finsler geometry the complete lift vector fields have distinguished geometric significance. For example a vector field on a Finsler manifold is said to be conformal if its complete lift is conformal in usual sense. In this work we define a new Riemannian or Pseudo-Riemannian metric on TM derived from a Finsler metri…

We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.

The study finds points on surfaces where a tensor is conformal to a metric.

Study on para-Sasakian metrics and their solitons.

The paper defines and analyzes conformal trajectories in 3D space forms.

New proof shows all conformal vector fields on complex hyperbolic space are Killing.

The paper characterizes Clairaut conformal submersions on Ricci solitons.

Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some n…

Paper extends isoperimetric inequalities for non-starshaped hypersurfaces.

Classifies hypersurfaces with specific curvature properties in 4D space.

Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection ('pull-back formalism'), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. …