Superconnections and An Intrinsic Gauss-Bonnet-Chern Formula for Finsler   Manifolds
  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. 
Huitao Feng, Ming Li
math.DG