Superconnections and An Intrinsic Gauss-Bonnet-Chern Formula for Finsler Manifolds

Abstract

In this paper, we establish an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds by using the Mathai-Quillen's superconnection formalism, in which no extra vector field is involved. Furthermore, we prove a more general Lichnerowicz formula in this direction through a geometric localization procedure.

35 pages. Title changed. In this revised version, we complete the geometric localization procedure and then obtain a more general Lichnerowicz formula