On the eigenvalues of the twisted Dirac operator

Author(s)

Jardim, Marcos ^[1] ; Leao, Rafael F. ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Dept Math, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 50, n. 6 JUN 2009.
• Web of Science Citations: 3

Abstract

Given a compact Riemannian spin manifold whose untwisted Dirac operator has trivial kernel, we find a family of connections del(At) for t is an element of {[}0,1] on a trivial vector bundle of rank no larger than dim M+1, such that the first eigenvalue of the twisted Dirac operator D(At) is nonzero for t not equal 1 and vanishes for t = 1. However, if one restricts the class of twisting connections considered, then nonzero lower bounds do exist. We illustrate this fact by establishing a nonzero lower bound for the Dirac operator twisted by Hermitian-Einstein connections over Riemann surfaces. (C) 2009 American Institute of Physics. {[}DOI: 10.1063/1.3133944] (AU)

• FAPESP's process: 05/04558-0 - Symmetries in geometry, topology and mathematical physics
• Grantee: Alcibiades Rigas
• Support Opportunities: Research Projects - Thematic Grants