Generic metrics and the mass endomorphism on spin three-manifolds

Abstract

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.

8 pages

References in corpus (2)

• On the Spinor Representation of Surfaces in Euclidean 3-Space
• On nodal sets for Dirac and Laplace operators

Cited by in corpus (1)

• The Cauchy problems for Einstein metrics and parallel spinors