scholarly journals A Characterization of Complex Projective Spaces by Sections of Line Bundles

2015 ◽  
Vol 05 (08) ◽  
pp. 450-453
Author(s):  
Shuyu Liang ◽  
Yanan Gao ◽  
Yicai Zhao
Keyword(s):  
Projective Spaces ◽  
Line Bundles ◽  
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.

scholarly journals The index of harmonic maps from surfaces to complex projective spaces

2020 ◽  
Vol 31 (09) ◽  
pp. 2050069
Author(s):  
J. Oliver
Keyword(s):  
Projective Space ◽  
Lower Bounds ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Projective Spaces ◽  
Line Bundles ◽  
Complex Projective Spaces ◽  
Holomorphic Sections ◽  
Higher Genus ◽  
Complex Projective

We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases from higher genus surfaces.

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