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Parallel submanifolds of complex projective space and their normal holonomy

Parallel submanifolds of complex projective space and their normal holonomy The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using a normal holonomy approach. Indeed, we explain how these submanifolds can be regarded as the unique complex orbits of the (projectivized) isotropy representation of an irreducible Hermitian symmetric space. Moreover, we show how these important submanifolds are related to other areas of mathematics and theoretical physics. Finally, we state a conjecture about the normal holonomy group of a complete and full complex submanifold of the complex projective space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Parallel submanifolds of complex projective space and their normal holonomy

Mathematische Zeitschrift , Volume 261 (1) – Jan 22, 2008

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References (38)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer-Verlag
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-008-0307-8
Publisher site
See Article on Publisher Site

Abstract

The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using a normal holonomy approach. Indeed, we explain how these submanifolds can be regarded as the unique complex orbits of the (projectivized) isotropy representation of an irreducible Hermitian symmetric space. Moreover, we show how these important submanifolds are related to other areas of mathematics and theoretical physics. Finally, we state a conjecture about the normal holonomy group of a complete and full complex submanifold of the complex projective space.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jan 22, 2008

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