Real hypersurfaces of quaternionic projective space satisfying ▽UiR = 0
Juan de Dios Pérez,Young Jin Suh +1 more
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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
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Real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator is of Codazzi type
I. Jeong,H. H. Lee,Young Jin Suh +2 more
TL;DR: In this article, a non-existence theorem for Hopf hypersurfaces in complex two-plane Grassmannians G 2 (ℂm+2) whose structure Jacobi operator R ξ is of Codazzi type was proved.
Journal ArticleDOI
Pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians
TL;DR: In this paper, a complete classification of Hopf pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians G 2 (ℂ m +2 ) is given.
Journal ArticleDOI
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator
TL;DR: In this article, the authors studied the classifying problem of immersed submanifolds in Hermitian symmetric spaces and proved non-existence of real hypersurfaces in G2(ℂm+2) with generalized Tanaka-Webster parallel normal Jacobi operator.
Journal ArticleDOI
Hopf hypersurfaces in complex two-plane grassmannians with lie parallel normal jacobi operator
TL;DR: For Hopf hypersurfaces in the complex two-plane Grassmannian G2(C) with Lie parallel normal Jacobi operator R̄N and totally geodesic D and D ⊥ components of the Reeb flow, the authors gave some non-existence theorems.
Journal ArticleDOI
Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb invariant Ricci tensor☆
Gyu Jong Kim,Young Jin Suh +1 more
TL;DR: In this paper, the curvature tensor of a real hypersurface M in complex hyperbolic two-plane Grassmannians SU 2, m/S (U 2 ⋅ U m ), m ≥ 2 from the equation of Gauss was derived.
References
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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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