Spinc Structures and Scalar Curvature Estimates |
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Authors: | S Goette U. Semmelmann |
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Affiliation: | (1) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72070 Tübingen, Germany;(2) Mathematisches Institut, Universität München, Theresienstr. 39, D-80333, München, Germany |
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Abstract: | In this note, we look at estimates for the scalar curvature of a compact, connected Riemannian manifold Mwhich are related to spinc Dirac operators.We show that one may not enlarge a Kähler metric with positiveRicci curvature without making smaller somewhere on M.More generally, if f: N M is an area-nonincreasing map of a certain topological type,then the scalar curvature k of Ncannot be everywhere larger than f.If k f, then N is isometric to M × F, where F possesses a parallel untwisted spinor.We also give explicit upper bounds for min for arbitrary Riemannian metrics on certainsubmanifolds of complex projective space.In certain cases, these estimates are sharp:we give examples where equality is obtained. |
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Keywords: | algebraic varieties extremal metrics Kä hler metrics scalar curvature rigidity |
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