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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Commuting structure jacobi operator for hopf hypersurfaces in complex two-plane grassmannians
TL;DR: In this article, the authors classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other J operator or with the normal J operator.
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Real hypersurfaces in the complex quadric with generalized Killing shape operator
TL;DR: In this article, the authors introduced a notion of generalized Killing shape operator and its geometric meaning on real hypersurfaces in the complex quadric and gave a non-existence theorem for a Hopf real- hypersurface with generalized killing shape operator.
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A new classification on parallel Ricci tensor for real hypersurfaces in the complex quadric
Hyunjin Lee,Young Jin Suh +1 more
TL;DR: In this paper, the authors introduced the notion of parallel Ricci tensor for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2 and showed that the unit normal vector field N is singular.
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Generalized Killing–Ricci Tensor for Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians
TL;DR: In this article, a new notion of generalized Killing-Ricci tensor for real hypersurface M in complex hyperbolic two-plane Grassmannians was introduced.
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Ricci soliton and pseudo-Einstein real hypersurfaces in the complex hyperbolic quadric
TL;DR: In this paper, a new notion of Ricci-soliton and pseudo-Einstein for real hypersurfaces in the noncompact complex hyperbolic quadric S O 2, m 0 ∕ S O2 S O m.
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.
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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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