Real hypersurfaces of quaternionic projective space satisfying ▽UiR = 0
Juan de Dios Pérez,Young Jin Suh +1 more
TLDR
In this paper, the authors classify real hypersurfaces of quaternionic projective space whose curvature tensor is parallel in the direction of a 3D distribution, and they show that there are real hypersurifaces with parallel curvature vectors in quaternion projective spaces.Abstract:
It is known that there do not exist real hypersurfaces with parallel curvature tensor in quaternionic projective spaces. In this paper we classify real hypersurfaces of quaternionic projective space whose curvature tensor is parallel in the direction of certain 3-dimensional distribution.read more
Citations
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Journal ArticleDOI
Real hypersurfaces in complex space forms concerned with the local symmetry
TL;DR: In this paper, the Hopf fibration of a real hypersurface M in complex space form M m(4e) has been studied and a complete classification of real hypersuri surfaces in M m (4e), which satisfy the above geometric facts is given.
Journal ArticleDOI
Reeb lie derivatives on real hypersurfaces in complex hyperbolic two-plane Grassmannians
Eunmi Pak,Gyu Jong Kim +1 more
TL;DR: In this article , the authors considered a complex hyperbolic two-plane Grassmannian SU2,m/S(U2?Um) and gave a complete classification of Hopf real hypersurfaces with the above condition.
Journal ArticleDOI
Basic Inequalities for Real Hypersurfaces in Some Grassmannians
TL;DR: In this paper, the authors obtained some basic inequalities for real hypersurfaces of complex two-plane Grassmannians and complex hyperbolic 2-planar Grassmannian for both real and complex 2-plane surfaces.
Isometric Reeb Flow and Related Results on Hermitian Symmetric Spaces of Rank 2
TL;DR: Suh et al. as mentioned in this paper showed that Isometric Reeb Flow on Hermitian Symmetric Spaces of Rank 2 can be used to construct complex quadratic real hypersurfaces in Q2k tubes around the totally geodesic CPk.
Book ChapterDOI
Parallelism on Jacobi Operators for Hopf Hypersurfaces in Complex Two-Plane Grassmannians
Eunmi Pak,Young Jin Suh +1 more
TL;DR: In this article, a new notion of parallel Jacobi operator for real hypersurfaces in complex two-plane Grassmannians was proposed, and the generalized Tanaka-Webster connection was considered.
References
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Journal ArticleDOI
Quaternion Kählerian manifolds
TL;DR: Alekseevskii et al. as mentioned in this paper studied quaternion Kahlerian manifolds by using tensor calculus and obtained many interesting results. But they did not define a manifold as a Riemannian manifold which admits a bundle V of tensors of type (1, 1) having some properties.
Journal Article
Real hypersurfaces in quaternionic space forms.
TL;DR: In this paper, it was shown that in non-Euclidean spaces of constant holomorphic sectional curvature the curvature-adapted (real) hypersurfaces are exactly the Hopf hypersurface.
Journal ArticleDOI
Real hypersurfaces in quaternionic projective space
TL;DR: In this article, a systematic study of real hypersurfaces of quaternionic projective space using focal set theory was made, and the Ricci tensor of such hypersurface was studied.
Journal ArticleDOI
Real hypersurfaces of quaternionic projective space satisfying $$\nabla _{U_i } A = 0$$
TL;DR: In this paper, real hypersurfaces of quaternionic projective space satisfying the following properties were classified: 1, 2, 3.1.2, 4.3.
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