A characterization of type $A$ real hypersurfaces in complex projective space

2013 ◽  
Vol 83 (4) ◽  
pp. 707-714 ◽  
Author(s):  
JUAN DE DIOS PEREZ ◽  
YOUNG JIN SUH
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Type A ◽  
Real Hypersurfaces ◽  
Complex Projective

scholarly journals REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE

2010 ◽  
Vol 53 (2) ◽  
pp. 347-358 ◽  
Author(s):  
SADAHIRO MAEDA ◽  
HIROO NAITOH
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Shape Operator ◽  
Type A ◽  
Real Hypersurfaces ◽  
Ruled Real Hypersurfaces ◽  
Shape Operators ◽  
Complex Projective ◽  
Invariant Shape

AbstractWe characterize real hypersurfaces of type (A) and ruled real hypersurfaces in a complex projective space in terms of two φ-invariances of their shape operators, and give geometric meanings of these real hypersurfaces by observing their some geodesics.

Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie 𝔻-parallel

2013 ◽  
Vol 56 (2) ◽  
pp. 306-316 ◽  
Author(s):  
Juan de Dios Pérez ◽  
Young Jin Suh
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Jacobi Operator ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Complex Projective

AbstractWe prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie 𝔻-parallel and satisfies a further condition.

scholarly journals A note on real hypersurfaces of a complex projective space

1989 ◽  
Vol 47 (1) ◽  
pp. 108-113 ◽  
Author(s):  
Jung-Hwan Kwon ◽  
Hisao Nakagawa
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Real Hypersurfaces ◽  
Harmonic Curvature ◽  
Complex Projective

AbstractWe study real hypersurfaces of a complex projection space and show that there are no such hypersurfaces with harmonic curvature on which the structure vector is principal.

scholarly journals Geometric applications of critical point theory to submanifolds of complex projective space

1974 ◽  
Vol 55 ◽  
pp. 5-31 ◽  
Author(s):  
Thomas E. Cecil
Keyword(s):  
Projective Space ◽  
Critical Point ◽  
Distance Function ◽  
Complex Projective Space ◽  
Euclidean Distance ◽  
Point Theory ◽  
Euclidean Distance Function ◽  
Complex Projective ◽  
Class Of Functions

In a recent paper, [6], Nomizu and Rodriguez found a geometric characterization of umbilical submanifolds Mn ⊂ Rn+p in terms of the critical point behavior of a certain class of functions Lp, p ⊂ Rn+p, on Mn. In that case, if p ⊂ Rn+p, x ⊂ Mn, then Lp(x) = (d(x,p))2, where d is the Euclidean distance function.

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