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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

Chapter:
(p.268) 18 Holomorphic submanifolds, holomorphic sections and curvature
Source:
Differential Geometry
Author(s):

Clifford Henry Taubes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605880.003.0018

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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