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 the complex hyperbolic quadric with Reeb parallel shape operator
Young Jin Suh,Doo Hyun Hwang +1 more
TL;DR: In this paper, the authors introduced the notion of shape operator of Codazzi type for real hypersurfaces in the complex quadric and gave a complete proof of non-existence of real hypersuran surfaces in the case of this paper.
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Generalized Killing Ricci tensor for real hypersurfaces in complex two-plane Grassmannians
TL;DR: In this article, a new notion of generalized Ricci tensor for real hypersurfaces in complex two-plane Grassmannians G 2 ( ℂ m + 2 ) was introduced.
Journal ArticleDOI
Real Hypersurfaces with Killing Shape Operator in the Complex Quadric
TL;DR: In this paper, the notion of Killing shape operator for real hypersurfaces in the complex quadric was introduced, which implies that the unit normal vector field N becomes either the principal or isotropic.
Journal ArticleDOI
Recurrent real hypersurfaces in complex two-plane Grassmannians
TL;DR: In this article, the authors introduced the notion of recurrent shape operator for real hypersurface M in the complex two-plane Grassmannians G2(Cm+2) and gave a non-existence property of real hypersuran surfaces in G 2 (Cm + 2) with the recurrent shape operators.
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Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type
TL;DR: In this paper, the authors prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.
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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