The Euler Class from a General Connection, Relative to a Metric

2021/01/17 by Klatt, Brian
#53C05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.06791

Abstract

We extend the well-known formula for the Euler class of a real oriented even-dimensional vector bundle in terms of the curvature of a metric connection to the case of a general linear connection provided a metric is present. We rewrite the classical Gauss-Bonnet theorem in dimension two in light of this formula. We also discuss a potential application to a conjecture of Chern, and make a brief digression to discuss m-quasi-Einstein manifolds.

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