scholarly journals ON A COMPACT AND MINIMAL REAL HYPERSURFACE IN A QUATERNIONIC PROJECTIVE SPACE

2005 ◽  
Vol 42 (2) ◽  
pp. 327-335
Author(s):  
YEONG-WU CHOE ◽  
IMSOON JEONG
Keyword(s):  
Projective Space ◽  
Real Hypersurface ◽  
Quaternionic Projective Space

𝔇⊥-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection

2020 ◽  
Vol 20 (2) ◽  
pp. 163-168
Author(s):  
Eunmi Pak ◽  
Young Jin Suh
Keyword(s):  
Projective Space ◽  
Real Hypersurface ◽  
Jacobi Operator ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space ◽  
Totally Geodesic ◽  
Open Part ◽  
Jacobi Operators ◽  
Hopf Hypersurfaces ◽  
Normal Jacobi Operator

AbstractWe study classifying problems for real hypersurfaces in a complex two-plane Grassmannian G2(ℂm+2). In relation to the generalized Tanaka–Webster connection, we consider a new concept of parallel normal Jacobi operator for real hypersurfaces in G2(ℂm+2) and prove that a real hypersurface in G2(ℂm+2) with generalized Tanaka–Webster 𝔇⊥-parallel normal Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍPn in G2(ℂm+2), where m = 2n.

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Eunmi Pak ◽  
Young Suh
Keyword(s):  
Projective Space ◽  
Real Hypersurface ◽  
Jacobi Operator ◽  
Parallel Structure ◽  
Quaternionic Projective Space ◽  
Structure Jacobi Operator ◽  
Totally Geodesic ◽  
Open Part ◽  
Hopf Hypersurfaces

AbstractRegarding the generalized Tanaka-Webster connection, we considered a new notion of $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G 2(ℂm+2) and proved that a real hypersurface in G 2(ℂm+2) with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍP n in G 2(ℂm+2), where m = 2n.

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 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.

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