Related papers: Statistical conformal Killing Vector Fields for FL…
In this paper, we first investigate almost Yamabe solitons on compact Riemannian manifolds without boundary of dimension greater than or equal to two. We provide some sufficient conditions for which the defining conformal vector field…
Stationary and axially symmetric space-times play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum sub-class of these space-times is known as Weyl's class, and contains the…
Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we…
Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic…
In this paper, conformal motions are studied in plane symmetric static spacetimes. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these spacetimes are presented. All…
On a closed, connected Riemannian manifold with a K\"ahler foliation of codimension $q=2m$, any transverse Killing $r\ (\geq 2)$-form is parallel (S. D. Jung and M. J. Jung [\ref{JJ2}], Bull. Korean Math. Soc. 49 (2012)). In this paper, we…
We analyze Killing Initial Data on Cauchy surfaces in conformally rescaled vacuum space-times satisfying Friedrich's conformal field equations. As an application, we derive the KID equations on a spacelike $\mathcal{J}^-$.
We discuss the existence of Killing tensors for certain (physically motivated) stationary and axially symmetric vacuum space-times. We show nonexistence of a nontrivial Killing tensor for a Tomimatsu-Sato metric (up to valence 7), for a…
We analyze the space-times admitting two shear-free geodesic null congruences. The integrability conditions are presented in a plain tensorial way as equations on the volume element $U$ of the time-like 2--plane that these directions…
The collapsing dynamics of relativistic fluid are explored in $f(R)$ gravity in a detailed systematic manner for the non-static spherically symmetric spacetime satisfying the equation of the conformal Killing vector. With quasi-homologous…
In this paper, we show that some five-dimensional rotating black hole solutions of both gauged and ungauged supergravity, with independent rotation parameters and three charges admit separable solutions to the massless Hamilton-Jacobi and…
The Newman-Penrose equations for spacetimes having one spacelike Killing vector are reduced -- in a geometrically defined "canonical frame'' -- to a minimal set, and its differential structure is studied. Expressions for the frame vectors…
We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the…
We realize an explicit conformal mapping between the state and operator pictures in a class of (2+1)-dimensional non-Lorentzian field theories with SU(1,2)$\times$U(1) conformal symmetry. The state picture arises from null reducing…
In this article, we study mixed Killing vector fields, defined by the condition $L_V L_V g = f\, L_V g$, on the Cigar Ricci--Bourguignon soliton. While conformal vector fields are always mixed Killing, the converse fails in flat and open…
The formal solution of the second order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is…
We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci…
The present article provides a study of $2-$Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson-Walker space-times. Some conditions for a $2-$Killing…
The solutions of generalized Killing equation have been obtained for line element with initial $t^2 \oplus so(3)$ symmetry. The coefficients of the metric $g$ corresponding to these vector fields are written down.
We consider conformal Killing-Yano forms corresponding to the antisymmetric generalizations of conformal Killing vectors to higher degree forms in the presence of skew-symmetric torsion. Integrability conditions for torsionful conformal…