Annals of Global Analysis and Geometry

, Volume 17, Issue 4, pp 341–370

Generalized Killing Spinors and Conformal Eigenvalue Estimates for Spinc Manifolds

  • Marc Herzlich
  • Andrei Moroianu
Article

DOI: 10.1023/A:1006546915261

Cite this article as:
Herzlich, M. & Moroianu, A. Annals of Global Analysis and Geometry (1999) 17: 341. doi:10.1023/A:1006546915261

Abstract

In this paper we prove the Spinc analog of the Hijazi inequality on the first eigenvalue of the Dirac operator on compact Riemannian manifolds and study its equality case. During this study, we are naturally led to consider generalized Killing spinors on Spinc manifolds and we prove that such objects can only exist on low-dimensional manifolds (up to dimension three). This allows us to give a nice geometrical description of the manifolds satisfying the equality case of the above-mentioned inequality and to classify them in dimension three and four.

conformal eigenvalue estimates Killing spinors 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Marc Herzlich
    • 1
  • Andrei Moroianu
    • 2
  1. 1.Département de MathématiquesUniversité Montpellier II (Géométrie-Topologie et Algèbre, UPRESE du 5030 CNRS)MontpellierFrance
  2. 2.Centre de MathématiquesÉcole PolytechniquePalaiseauFrance