The Greiner's approach to heat kernel asymptotics and the variation formulas for the equivariant Ray-Singer metric
Yong Wang
TL;DR
This paper employs Greiner's heat kernel asymptotics to provide new proofs of key formulas related to the equivariant Ray-Singer metric, enhancing understanding of geometric invariants.
Contribution
It introduces novel proofs of the equivariant Gauss-Bonnet-Chern and Ray-Singer metric variation formulas using heat kernel techniques.
Findings
New proofs of equivariant Gauss-Bonnet-Chern formula
Variation formulas for equivariant Ray-Singer metric
Application of Greiner's approach to geometric analysis
Abstract
In this paper, using the Greiner's approach to heat kernel asymptotics, we give new proofs of the equivariant Gauss-Bonnet-Chern formula and the variation formulas for the equivariant Ray-Singer metric, which are originally due to J. M. Bismut and W. Zhang.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Operator Algebra Research · Geometry and complex manifolds