The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr black holes are isosp...

We give a Lorentzian metric on the null congruence associated with a timelike conformal vector field. A Liouville type theorem is proved and a boundedness for the volume of the null congruence, analogous to a well-known Berger-Green theorem in the Riemannian case, will be derived by studying conjugate points along null geodesics. As a consequence, several classification results on certain compa...

This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which all...

We prove that for every Q-homological Finsler 3-sphere (M,F ) with a bumpy and irreversible metric F , either there exist two non-hyperbolic prime closed geodesics, or there exist at least three prime closed geodesics.

Ordinary differential equation (ODE) models, e.g. the susceptible-infected-recovered model, are widely used in engineering, ecology, and epidemiology. Many ODE models

This article is concerned with geodesics in spaces of Hermitian metrics of positive curvature on an ample line bundle L → X over a Kähler manifold. Stimulated by a recent article of Phong-Sturm [PS], we study the convergence as N → ∞ of geodesics on the finite dimensional symmetric spaces HN of Bergman metrics of ‘height N ’ to Monge-Ampére geodesics on the full infinite dimensional symmetric s...

In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Fin...

In this paper, we investigate the surfaces generated by binormal motion of Bertrand curves, which is called Razzaboni surface, in Minkowski 3-space. We discussed the geometric properties of these surfaces in M according to the character of Bertrand geodesics. Then, we define the Razzaboni transformation for a given Razzaboni surface. In other words, we prove that there exists a dual of Razzabon...

We consider a class of exact solutions which represent nonexpanding impulsive waves in backgrounds with nonzero cosmological constant. Using a convenient 5-dimensional formalism it is shown that these spacetimes admit at least three global Killing vector fields. The same geometrical approach enables us to find all geodesics in a simple explicit form and describe the effect of impulsive waves on...

We derive a second-order ordinary differential equation (ODE), which is the limitof Nesterov’s accelerated gradient method. This ODE exhibits approximate equiv-alence to Nesterov’s scheme and thus can serve as a tool for analysis. We show thatthe continuous time ODE allows for a better understanding of Nesterov’s scheme.As a byproduct, we obtain a family of schemes with similar ...