Pseudo-Finsler Manifolds

Abstract

This chapter reviews the main topics of the geometry of pseudo-Finsler manifolds. It gives the basic background needed in the rest of the book. Here, we use the vertical vector bundle to develop a Finsler tensorial calculus. We define the main geometric objects necessary for the study of Finsler geometry. In particular, we describe in detail the Berwald, Cartan, and Rund connections. Finally, we give a new setting for pseudo-Finsler manifolds of constant curvature and present some special pseudo-Finsler manifolds.