Spin^c Structures and Scalar Curvature Estimates

Abstract

In this note, we look at estimates for the scalar curvature k of a Riemannian manifold M which are related to spin^c Dirac operators: We show that one may not enlarge a Kaehler metric with positive Ricci curvature without making k smaller somewhere on M. We also give explicit upper bounds for min(k) for arbitrary Riemannian metrics on certain submanifolds of complex projective space. In certain cases, these estimates are sharp: we give examples where equality is obtained.

19 pages, AmSTeX

Cited by in corpus (4)

• Scalar curvature estimates for compact symmetric spaces
• Scalar Curvature Estimates by Parallel Alternating Torsion
• Extremality and rigidity for scalar curvature in dimension four
• Generalized positive scalar curvature on spin${}^c$ manifolds