scholarly journals A~characterization of a~certain real hypersurface of type $({\rm A}_2)$ in a~complex projective space

2017 ◽  
Vol 67 (1) ◽  
pp. 271-278
Author(s):  
Byung Hak Kim ◽  
In-Bae Kim ◽  
Sadahiro Maeda
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Real Hypersurface ◽  
Complex Projective

scholarly journals A MINIMAL REAL HYPERSURFACE OF A COMPLEX PROJECTIVE SPACE WITH NONNEGATIVE SECTIONAL CURVATURE

2010 ◽  
Vol 81 (3) ◽  
pp. 488-492
Author(s):  
MAYUKO KON
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Complex Projective Space ◽  
Real Hypersurface ◽  
Nonnegative Sectional Curvature ◽  
Complex Projective

AbstractWe give a characterization of a minimal real hypersurface with respect to the condition for the sectional curvature.

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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