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Homogeneous structures on Kähler submanifolds of complex projective spaces*

Published online by Cambridge University Press:  20 January 2009

Sergio Console  and
Anna Fino
Sergio Console
Affiliation:
Dipartimento di MatematicaUniversita di Torinovia Carlo Alberto, 10, I-10123 Torino e-mail console@dm.unito.it / fino@dm.unito.it
Anna Fino
Affiliation:
Dipartimento di MatematicaUniversita di Torinovia Carlo Alberto, 10, I-10123 Torino e-mail console@dm.unito.it / fino@dm.unito.it
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Abstract

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In this paper we give a differential characterization of homogeneous Kähler submanifolds of complex projective spaces in terms of the existence of a tensor field, the homogeneous structure S. We show that for any m∈M, Sm determines a unitary representation whose orbit at m is a compact, complete Kähler submanifold which extends M. We consider the U(n) × U(N ~ n) (n = dim ℂM) module of the space of these tensors and we find its irreducible factors.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 381 - 395
Copyright
Copyright © Edinburgh Mathematical Society 1996

Footnotes

*

Work partially supported by the GNSAGA of CNR and by the MURST of Italy.

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