Normalized submanifolds with flat normal connection in projective space

1983 ◽  
Vol 33 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A. V. Chakmazyan
Keyword(s):  
Projective Space ◽  
Normal Connection ◽  
Flat Normal Connection

scholarly journals Anti-invariant submanifolds with flat normal connection

1978 ◽  
Vol 13 (4) ◽  
pp. 577-588 ◽  
Author(s):  
Kentaro Yano ◽  
Masahiro Kon ◽  
Ikuo Ishihara
Keyword(s):  
Normal Connection ◽  
Flat Normal Connection ◽  
Invariant Submanifolds

scholarly journals PINCHING THEOREMS FOR A COMPACT MINIMAL SUBMANIFOLD IN A COMPLEX PROJECTIVE SPACE

2008 ◽  
Vol 77 (1) ◽  
pp. 99-114
Author(s):  
MAYUKO KON
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Fundamental Form ◽  
Additional Condition ◽  
Complex Projective Space ◽  
Second Fundamental Form ◽  
Minimal Submanifold ◽  
Normal Connection ◽  
The Second Fundamental Form ◽  
Complex Projective

AbstractWe give a formula for the Laplacian of the second fundamental form of an n-dimensional compact minimal submanifold M in a complex projective space CPm. As an application of this formula, we prove that M is a geodesic minimal hypersphere in CPm if the sectional curvature satisfies K≥1/n, if the normal connection is flat, and if M satisfies an additional condition which is automatically satisfied when M is a CR submanifold. We also prove that M is the complex projective space CPn/2 if K≥3/n, and if the normal connection of M is semi-flat.

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