scholarly journals A characterization of complex projective spaces by linear subspace sections

1977 ◽  
Vol 1 (0) ◽  
pp. 157-162 ◽  
Author(s):  
Mitsuhiro Itoh
Keyword(s):  
Linear Subspace ◽  
Projective Spaces ◽  
Complex Projective Spaces ◽  
Complex Projective

scholarly journals Homogeneous structures on Kähler submanifolds of complex projective spaces

1996 ◽  
Vol 39 (2) ◽  
pp. 381-395 ◽  
Author(s):  
Sergio Console ◽  
Anna Fino
Keyword(s):  
Unitary Representation ◽  
Tensor Field ◽  
Projective Spaces ◽  
Homogeneous Structure ◽  
Complex Projective Spaces ◽  
Homogeneous Structures ◽  
Kähler Submanifolds ◽  
Complex Projective

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.

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