scholarly journals A new characterization of the Berger sphere in complex projective space

2015 ◽  
Vol 92 ◽  
pp. 129-139 ◽  
Author(s):  
Haizhong Li ◽  
Luc Vrancken ◽  
Xianfeng Wang
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Berger Sphere ◽  
Complex Projective

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.

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.

On Characterization of Hypersurfaces of Degrees 2 and 3 in the Complex Projective Space

1986 ◽  
Vol 29 (1) ◽  
pp. 74-78
Author(s):  
Michal Szurek
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Complex Projective

RésuméLe but de cette note est de proposer une caractérisation des espaces projectifs complexes, des hyperquadriques et des hypersurfaces du troisième degré dans Pnc à l'aide de leurs points d'intersection avec l'ensemble des zéros d'une section d'un fibre positif donné sur la variété ambiante. Ceci généralise et complète ainsi certains résultats présentés par Badescu et Itoh.

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