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Differential GeometryBundles, Connections, Metrics and Curvature$
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Clifford Henry Taubes

Print publication date: 2011

Print ISBN-13: 9780199605880

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199605880.001.0001

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Holomorphic submanifolds, holomorphic sections and curvature

Holomorphic submanifolds, holomorphic sections and curvature

(p.268) 18 Holomorphic submanifolds, holomorphic sections and curvature
Differential Geometry

Clifford Henry Taubes

Oxford University Press

This chapter discusses how complex manifolds and Kähler manifolds can appear as submanifolds in a larger complex or Kähler manifold. It describes holomorphic submanifolds of a complex manifold and holomorphic submanifolds of projective spaces. It gives a proof on holomorphic submanifolds in ℂℙn. It also explains the curvature of a Kähler metric; curvature with no (0, 2) part and holomorphic sections. Finally, it gives an example on ℂℙn.

Keywords:   complex manifolds, projective spaces, curvatures, Kähler manifolds

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