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.

scholarly journals Constant curved minimal CR 3-spheres in CPn

2005 ◽  
Vol 79 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Zhen-Qi Li ◽  
An-Min Huang
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Complex Projective Space ◽  
Constant Sectional Curvature ◽  
Full Dimension ◽  
Analytic Expression ◽  
Complex Projective

AbstractIn this paper we prove that minimal 3-spheres of CR type with constant sectional curvature c in the complex projective space CPn are all equivariant and therefore the immersion is rigid. The curvature c of the sphere should be c = 1/(m2-1) for some integer m≥ 2, and the full dimension is n = 2m2-3. An explicit analytic expression for such an immersion is given.

scholarly journals THE MINIMAL WITH CONSTANT SECTIONAL CURVATURE IN

2015 ◽  
Vol 99 (1) ◽  
pp. 63-75 ◽  
Author(s):  
SEN HU ◽  
KANG LI
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Constant Curvature ◽  
Complex Projective Space ◽  
Constant Sectional Curvature ◽  
Complex Projective

It is known that the minimal 3-spheres of CR type with constant sectional curvature have been classified explicitly, and also that the weakly Lagrangian case has been studied. In this paper, we provide some examples of minimal 3-spheres with constant curvature in the complex projective space, which are neither of CR type nor weakly Lagrangian, and give the adapted frame of a minimal 3-sphere of CR type with constant sectional curvature.

scholarly journals Kählerian submanifolds in a complex projective space with second fundamental form of polynomial type

1984 ◽  
Vol 96 ◽  
pp. 61-70
Author(s):  
Ryoichi Takagi
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Covariant Derivative ◽  
Complex Projective Space ◽  
Second Fundamental Form ◽  
Holomorphic Sectional Curvature ◽  
Fundamental Tensor ◽  
Polynomial Type ◽  
Complex Projective

Let PN be an iV-dimensional complex projective space with Fubini-Study metric of constant holomorphic sectional curvature, and M be a Kählerian submanifold in PN. Let H be the second fundamental tensor + of M, and be the covariant derivative of type (1, 0) on M.

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