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
Citations
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Real hypersurfaces in the complex quadric with commuting and parallel Ricci tensor
TL;DR: In this article, the authors introduced the notion of commuting and parallel Ricci tensor for real hypersurfaces in the complex quadric Q m = S O m + 2 /S O 2 S O O m.
Journal ArticleDOI
On real hypersurfaces with η-parallel curvature tensor in complex space forms
TL;DR: In this paper, the authors give a complete classification of real hypersurfces M in complex space forms Mn(c), c≠0 in terms of an η-parallel curvature tensor and a certain commutative condition defined on the distribution T0={X∈TxM| X⊥ξ} of M in Mn (c).
Journal ArticleDOI
On real hypersurfaces in a quaternionic hyperbolic space in terms of the derivative of the second fundamental tensor
TL;DR: In this article, a characterization of real hypersurfaces of type A0, A in a quaternionic hyperbolic space was given by the covariant derivative of the second fundamental tensor.
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Real Hypersurfaces in the Complex Quadric with Reeb Parallel Ricci Tensor
Young Jin Suh,Young Jin Suh +1 more
TL;DR: In this paper, the authors introduced the notion of commuting and parallel Ricci tensor for real hypersurfaces in the complex quadric, where the Reeb-Ricci tensors were used to classify real hypersuran surfaces with and without Reeb normal vector fields.
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Real hypersurfaces in the complex quadric with Reeb invariant Ricci tensor
TL;DR: In this article, the Reeb invariant Ricci tensor was introduced for real hypersurfaces in the complex quadric Q m = S O m + 2 ∕ s O m S O 2.
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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