arXiv research

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.

The study classifies spaces with specific conformal vector fields.

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…

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…

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

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.

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.

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.

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…

Conditions for Riemannian manifolds to be Euclidean spheres or spaces.

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.

Local Lorentzian theorem preserves metrics or makes them flat.

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 study classifies gradient Ricci solitons with specific vector fields.

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

The paper characterizes Clairaut conformal submersions on Ricci solitons.

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. …

Study on Yamabe solitons on specific complex manifolds, focusing on torse-forming vector fields.

We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…

The paper characterizes Kenmotsu manifolds with conformal η-Ricci solitons.

Study on vector fields on Lie groups reveals surprising algebraic coincidences.

We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their infinitesimal version, called bi-conformal vector fields. We show the differential co…

Study on Ricci-Bourguignon solitons on specific product spaces.

We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is conformally flat. In either case, the vector field is locally conjugate to a no…

The paper examines conditions for a vector field to be Killing in almost Yamabe solitons.

A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a Finsler manifold. We characterize a concircular vector field with some PDEs on t…