Rigidity theorems for holomorphic curves in a complex Grassmann manifold G(3,6)

2021 ◽  
pp. 2150095
Author(s):  
Jun Wang ◽  
Jie Fei
Keyword(s):  
Grassmann Manifold ◽  
Holomorphic Curves ◽  
Moving Frames ◽  
Local Rigidity ◽  
Complex Grassmann Manifold ◽  
Rigidity Theorems

In this paper, we prove some local rigidity theorems of holomorphic curves in a complex Grassmann manifold [Formula: see text] by moving frames. By applying our rigidity theorems, we also give a characterization of all homogeneous holomorphic two-spheres in [Formula: see text] classified by the second author.

scholarly journals Holomorphic curves in the complex quadric

1987 ◽  
Vol 35 (1) ◽  
pp. 125-148 ◽  
Author(s):  
Gary R. Jensen ◽  
Marco Rigoli ◽  
Kichoon Yang
Keyword(s):  
Holomorphic Curves ◽  
Local Theory ◽  
Moving Frames ◽  
Complex Quadric ◽  
Complex Hyperquadric ◽  
Method Of Moving Frames

A local theory of holomorphic curves in the complex hyperquadric is worked out using the method of moving frames. As a consequence a complete global characterization of totally isotropic curves is obtained.

scholarly journals Local rigidity theorems of 2-type hypersurfaces in a hypersphere

1991 ◽  
Vol 122 ◽  
pp. 139-148 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Finite Type ◽  
Position Vector ◽  
Constant Vector ◽  
Local Rigidity ◽  
Rigidity Theorems ◽  
Finite Sum

A submanifold M (connected but not necessary compact) of a Euclidean m-space Em is said to be of finite type if each component of its position vector X can be written as a finite sum of eigenfunctions of the Laplacian Δ of M, that is,where X0 is a constant vector and ΔXt = λtXt, t = 1, 2, · · ·, k. If in particular all eigenvalues {λ1, λ2, · · ·, λk are mutually different, then M is said to be of k-type (cf. [3] for details).

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