Related papers: Closed conformal Killing-Yano tensor and geodesic …
General higher-dimensional rotating black hole spacetimes of any dimensions admit the Killing and Killing-Yano tensors, which generate the hidden symmetries just as in four-dimensional Kerr spacetime. We study these properties of the black…
In this paper, we study the uniqueness of type II Yamabe metrics in conformal classes on a compact connected manifold with boundary, and we investigate Obata-type theorems for type II Yamabe metrics. In particular, we establish a theorem…
We investigate the structure of join tensors, which may be regarded as the multivariable extension of lattice-theoretic join matrices. Explicit formulae for a polyadic decomposition (i.e., a linear combination of rank-1 tensors) and a…
This paper presents an efficient technique for finding Killing, homothetic, or even proper conformal Killing vectors in the Newman-Penrose (NP) formalism. Leaning on, and extending, results previously derived in the GHP formalism we show…
We extend the study of the vacuum Einstein constraint equations on manifolds with ends of cylindrical type initiated by Chru\'sciel and Mazzeo by finding a class of solutions to the fully coupled system on such manifolds. We show that given…
In this article, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder $M\simeq S^1\times\mathbb{R}$ or a complete Riemannian plane $M\simeq\mathbb{R}^2$ leads to having…
The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically…
We study the Lie point symmetries of a general class of partial differential equations (PDE) of second order. An equation from this class naturally defines a second-order symmetric tensor (metric). In the case the PDE is linear on the first…
Important classes of null geodesics and hidden symmetries in the Sen black hole are investigated. First, we obtain the principal null geodesics and circular photon orbits. Then, an irreducible rank-two Killing tensor and a conformal Killing…
By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible…
On spaces of constant curvature, the geodesic equations automatically have higher order integrals, which are just built out of first order integrals, corresponding to the abundance of Killing vectors. This is no longer true for general…
We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal…
We study the integrability of the equations of motion for the Nambu-Goto strings with a cohomogeneity-one symmetry in Minkowski spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue…
Contact Riemannian manifolds, whose complex structures are not necessarily integrable, are generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection plays the role of the Tanaka-Webster connection of a…
In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat…
We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.
We generalize Killing equations to a test particle system which is subjected to external force. We relax the conservation condition by virtue of reparametrization invariance of a particle orbit. As a result, we obtain generalized Killing…
Generalized Kerr-NUT-de Sitter spacetime is the most general spacetime which admits a rank-2 closed conformal Killing-Yano tensor. It contains the higher-dimensional Kerr-de Sitter black holes with partially equal angular momenta. We study…
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…
The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any…