Iterated Segre mappings of real submanifolds in complex space and applications

2009 ◽  
pp. 1405-1419
Author(s):  
Linda Preiss Rothschild
Keyword(s):  
Complex Space ◽  
Real Submanifolds

Real Submanifolds in Complex Space and Their Mappings (PMS-47)

1999 ◽  
Author(s):  
M. Salah Baouendi ◽  
Peter Ebenfelt ◽  
Linda Preiss Rothschild
Keyword(s):  
Complex Space ◽  
Real Submanifolds

scholarly journals Local geometric properties of real submanifolds in complex space

2000 ◽  
Vol 37 (03) ◽  
pp. 309-337 ◽  
Author(s):  
M. S. Baouendi ◽  
P. Ebenfelt ◽  
Linda Preiss Rothschild
Keyword(s):  
Complex Space ◽  
Real Submanifolds ◽  
Geometric Properties

Totally real submanifolds in a generalized complex space form

2016 ◽  
Vol 10 (02) ◽  
pp. 1750035
Author(s):  
Majid Ali Choudhary
Keyword(s):  
Fundamental Form ◽  
Complex Space ◽  
Space Form ◽  
Second Fundamental Form ◽  
Text Structure ◽  
Complex Space Form ◽  
Real Submanifolds ◽  
Constant Length ◽  
Generalized Complex ◽  
Totally Real

In the present paper, we investigate totally real submanifolds in generalized complex space form. We study the [Formula: see text]-structure in the normal bundle of a totally real submanifold and derive some integral formulas computing the Laplacian of the square of the second fundamental form and using these formulas, we prove a pinching theorem. In fact, the purpose of this note is to generalize results proved in B. Y. Chen and K. Ogiue, On totally real manifolds, Trans. Amer. Math. Soc. 193 (1974) 257–266, S. S. Chern, M. Do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional Analysis and Related Fields (Springer-Verlag, 1970), pp. 57–75 to the case, when the ambient manifold is generalized complex space form.

scholarly journals Totally real submanifolds of a complex space form

1996 ◽  
Vol 19 (1) ◽  
pp. 39-44 ◽  
Author(s):  
U-Hang Ki ◽  
Young Ho Kim
Keyword(s):  
Mean Curvature ◽  
Complex Space ◽  
Space Form ◽  
Curvature Vector ◽  
Complex Space Form ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Real Submanifolds ◽  
Parallel Mean Curvature ◽  
Totally Real

Totally real submanifolds of a complex space form are studied. In particular, totally real submanifolds of a complex number space with parallel mean curvature vector are classified.

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