Superconnections and An Intrinsic Gauss-Bonnet-Chern Formula for Finsler Manifolds
Huitao Feng, Ming Li
TL;DR
This paper develops an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds using superconnection formalism, avoiding extra vector fields, and extends it with a generalized Lichnerowicz formula via geometric localization.
Contribution
It introduces a new intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds using superconnections, without involving additional vector fields, and generalizes it with a Lichnerowicz formula.
Findings
Established an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds.
Proved a generalized Lichnerowicz formula through geometric localization.
Demonstrated the effectiveness of superconnection formalism in Finsler geometry.
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.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows