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...

The geodesics for a sub-Riemannian metric on a threedimensional contact manifold M form a 1-parameter family of curves along each contact direction. However, a collection of such contact curves on M , locally equivalent to the solutions of a fourth-order ODE, are the geodesics of a sub-Riemannian metric only if a sequence of invariants vanish. The first of these, which was first identified by F...

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 investigate the Birman Series set in a neighborhood of a cusp on a punctured surface, showing that it is homeomorpic to a cantor set union countably many isolated points cross a line. The local topology of the cantor set is shown to be related in a simple way to the global behavior of simple geodesics. From this we deduce that a certain series is constant across the Teichmuller space 1. Intr...

Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two clo...

Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two clo...

The non-uniqueness of geodesics joining two given points in universal Teichm uller space is proved in the previous paper 7]. The purpose of the present paper is to discuss the non-uniqueness of geodesics in any innnite-dimensional Teichm uller space. It is proved that if 1 and 2 are two extremal Beltrami diierentials belonging to a point ] of a Teichm uller space and 1 ? 2 does not belong to N-...