Spin^c Structures and Scalar Curvature Estimates

Details Spin^c Structures and Scalar Curvature Estimates Spin^c Structures and Scalar Curvature Estimates

1999-05-14

arxiv.org/abs/math/9905089v2

Ann. Global Anal. Geom. 20, No. 4 (2001), 301-324

Mathematics

Differential Geometry

19 pages, AmSTeX

Scientific paper

10.1023/A:1013035721335

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.

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