The first conformal Dirac eigenvalue on 2-dimensional tori

JOURNAL OF GEOMETRY AND PHYSICS

卷:56

Article

Ammann, B ; Humbert, E

关键词: spin structure;    eigenvalue;    Dirac operator;    2-dimensional tori;   

DOI  :  10.1016/j.geomphys.2005.04.007

来源: Elsevier

【 摘 要 】

Let M be a compact manifold with a spin structure chi and a Riemannian metric g. Let lambda(2)(g) be the smallest eigenvalue of the square of the Dirac operator with respect to g and chi. The tau-invariant is defined as tau(M, chi) := sup inf root lambda(2)(g)Vol (M, g)(1/n) where the supremum runs over the set of all conformal classes on M, and where the infimum runs over all metrics in the given class. e show that tau(T-2, chi) = 2 root pi if chi is the non-trivial spin structure on T-2. In order to calculate this invariant, we study the infimum as a function on the spin-conformal moduli space and we show that the infimum converges to 2 root pi at one end of the spin-conformal moduli space. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free