Generic metrics and the mass endomorphism on spin three-manifolds

Details Generic metrics and the mass endomorphism on spin three-manifolds Generic metrics and the mass endomorphism on spin three-manifolds

2009-04-08

arxiv.org/abs/0904.1330v2

Ann. Global Anal. Geom. 37, 2, 163-171 (2010)

Mathematics

Differential Geometry

8 pages

Scientific paper

10.1007/s10455-009-9179-3

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.

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