scholarly journals A differentiable sphere theorem for compact Lagrangian submanifolds in complex Euclidean space and complex projective space

2014 ◽  
Vol 22 (2) ◽  
pp. 269-288 ◽  
Author(s):  
Haizhong Li ◽  
Xianfeng Wang
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Lagrangian Submanifolds ◽  
Sphere Theorem ◽  
Complex Euclidean Space ◽  
Complex Projective ◽  
Differentiable Sphere Theorem

scholarly journals On the deficiencies of meromorphic mappings of Cn into PNC

1977 ◽  
Vol 67 ◽  
pp. 165-176 ◽  
Author(s):  
Seiki Mori
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Meromorphic Mapping ◽  
Meromorphic Mappings ◽  
Complex Euclidean Space ◽  
Complex Projective

Let f(z) be a non-degenerate meromorphic mapping of the n-dimensional complex Euclidean space Cn into the N-dimensional complex projective space PNC. A generalization of results of Edrei-Fuchs [2] for meromorphic mappings of C into PNC was given by Toda [5], and an estimate of K(λ) for meromorphic mappings of Cn into PNC was done by Noguchi [4]. In this note we generalize several results of Edrei-Fuchs [2] in the case of meromorphic mappings of Cn into PNC.

Approximation by Rational Mappings, via Homotopy Theory

2006 ◽  
Vol 49 (2) ◽  
pp. 237-246 ◽  
Author(s):  
P. M. Gauthier ◽  
E. S. Zeron
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Homotopy Theory ◽  
Continuous Mappings ◽  
Complex Euclidean Space ◽  
Complex Projective ◽  
Compact Subsets

AbstractContinuous mappings defined from compact subsets K of complex Euclidean space ℂn into complex projective space ℙm are approximated by rational mappings. The fundamental tool employed is homotopy theory.

Lagrangian submanifolds in complex projective space CP n

2012 ◽  
Vol 7 (6) ◽  
pp. 1129-1140
Author(s):  
Xiaoxiang Jiao ◽  
Chiakuei Peng ◽  
Xiaowei Xu
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Lagrangian Submanifolds ◽  
Complex Projective

Characterizing warped-product Lagrangian immersions in complex projective space

2009 ◽  
Vol 52 (2) ◽  
pp. 273-286 ◽  
Author(s):  
J. Bolton ◽  
C. Rodriguez Montealegre ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Warped Product ◽  
Lagrangian Submanifolds ◽  
Lagrangian Submanifold ◽  
Horizontal Curve ◽  
Lagrangian Immersion ◽  
Complex Projective

AbstractStarting from two Lagrangian immersions and a horizontal curve in S3(1), it is possible to construct a new Lagrangian immersion, which we call a warped-product Lagrangian immersion. In this paper, we find two characterizations of warped-product Lagrangian immersions. We also investigate Lagrangian submanifolds which attain at every point equality in the improved version of Chen's inequality for Lagrangian submanifolds of ℂPn(4) as discovered by Opreaffi We show that, for n≥4, an n-dimensional Lagrangian submanifold in ℂPn(4) for which equality is attained at all points is necessarily minimal.

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