On the spectral geometry for the Jacobi operators of harmonic maps into a quaternionic projective space

1996 ◽  
Vol 60 (2) ◽  
Author(s):  
TaeHo Kang ◽  
JinSuk Pak
Keyword(s):  
Projective Space ◽  
Harmonic Maps ◽  
Spectral Geometry ◽  
Quaternionic Projective Space ◽  
Jacobi Operators

On the spectral geometry for the Jacobi operators of harmonic maps into C-manifolds

2006 ◽  
pp. 1893-1903
Author(s):  
Tae Ho Kang ◽  
Hyunsuk Kim ◽  
Tae Wan Kim
Keyword(s):  
Harmonic Maps ◽  
Spectral Geometry ◽  
Jacobi Operators

HARMONIC TWO-SPHERES IN THE SYMPLECTIC GROUP Sp(n)

2006 ◽  
Vol 17 (03) ◽  
pp. 295-311 ◽  
Author(s):  
RUI PACHECO
Keyword(s):  
Projective Space ◽  
Symplectic Group ◽  
Harmonic Maps ◽  
Point Of View ◽  
Quaternionic Projective Space ◽  
Alternative Characterization ◽  
Theoretic Point

We shall exploit the Grassmannian theoretic point of view introduced by Segal in order to study harmonic maps from a two-sphere into the symplectic group Sp(n). By using this methodology, we shall be able to deduce an "uniton factorization" of such maps and an alternative characterization of harmonic two-spheres in the quaternionic projective space ℍPn.

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.

The Construction of a Class of Harmonic Maps to Quaternionic Projective Space

1984 ◽  
Vol s2-30 (1) ◽  
pp. 151-159 ◽  
Author(s):  
James F. Glazebrook
Keyword(s):  
Projective Space ◽  
Harmonic Maps ◽  
Quaternionic Projective Space

scholarly journals A characterization of real hypersurfaces of quaternionic projective space

1991 ◽  
Vol 15 (2) ◽  
pp. 315-323
Author(s):  
J.D. Perez
Keyword(s):  
Projective Space ◽  
Real Hypersurfaces ◽  
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 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).

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