scholarly journals Sectional curvature of QR-submanifolds of (p-1) QR-dimension in a quaternionic projective space QP^{(n+p)/4}

2006 ◽  
pp. 1-16
Author(s):  
Yeong-Wu Choe ◽  
Imsoon Jeong ◽  
Jin Suk Pak ◽  
Hwal-Lan Yoo
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Quaternionic Projective Space

scholarly journals On real hypersurfaces in quaternionic projective space with𝒟⊥-recurrent second fundamental tensor

1999 ◽  
Vol 22 (1) ◽  
pp. 109-117
Author(s):  
Young Jin Suh ◽  
Juan De Dios Pérez
Keyword(s):  
Projective Space ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space ◽  
Fundamental Tensor ◽  
Orthogonal Distribution

In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective spaceQPmwith𝒟⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution𝒟.

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 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 A characterization of Einstein real hypersurfaces in quaternionic projective space

1998 ◽  
Vol 22 (1) ◽  
pp. 165-178
Author(s):  
Soo Hyo Lee ◽  
Juan de Dios Perez ◽  
Young Jin Suh
Keyword(s):  
Projective Space ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space

Naturally reductive homogeneous real hypersurfaces in quaternionic space forms

2003 ◽  
Vol 74 (1) ◽  
pp. 87-100
Author(s):  
Setsuo Nagai
Keyword(s):  
Projective Space ◽  
Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space ◽  
Space Forms ◽  
The Family ◽  
Quaternionic Hyperbolic Space ◽  
Quaternionic Space ◽  
Naturally Reductive

AbstractWe determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space HPn(n ≥ 3). We conclude that the naturally reductive curvature-adapted real hypersurfaces in HPn are Q-quasiumbilical and vice-versa. Further, we study the same problem in quaternionic hyperbolic space HHn(n ≥ 3).

scholarly journals On certain real hypersurfaces of quaternionic projective space

1991 ◽  
Vol 14 (1) ◽  
pp. 205-207 ◽  
Author(s):  
Juan De Dios Perez ◽  
Florentino G. Santos
Keyword(s):  
Projective Space ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space

We classify certain real hypersurfaces ot a quaternionic projective space satisfying the conditionσ(R(X,Y)SZ)=0.

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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