Complete space-like submanifolds in a de Sitter space with parallel mean curvature vector.
Complete space-like submanifolds with constant scalar curvature in a de Sitter space.
Complex hypersurfaces of a generalized manifold
Complex timelike isothermic surfaces and their geometric transformations.
Conformal nullity of isotropic submanifolds
We introduce and study submanifolds with extrinsic curvature and second fundamental form related by an inequality that holds for isotropic submanifolds and becomes equality for totally umbilical submanifolds. The dimension of umbilical subspaces and the index of conformal nullity of these submanifolds with low codimension are estimated from below. The corollaries are characterizations of extrinsic spheres in Riemannian spaces of positive curvature.
Conformally Flat Submanifolds of Euclidean Space.
Connections on embedded manifolds.
Conormal Bundles with Vanishing Maslov Form.
Constant Curvature 2-spheres in the 4-sphere.
Constant mean curvature hypersurfaces with constant -invariant.
Contact CR-doubly warped product submanifolds in Kenmotsu space forms.
Contact CR-Submanifolds of Kenmotsu Manifolds
2000 Mathematics Subject Classification: 53C15, 53C42.In this paper, we research some fundamental properties of contact CR-Submanifolds of a Kenmotsu manifold. We show that the anti-invariant distribution is always integrable and give a necessary and sufficient condition for the invariant distribution to be integrable. After then, properties of the induced structures on submanifold by almost contact metric structure on the ambient manifold are categorized. Finally, we give some results for contact...
Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form
The purpose of this paper is to study contact CR-submanifolds with nonvanishing parallel mean curvature vector immersed in a Sasakian space form. In §1 we state general formulas on contact CR-submanifolds of a Sasakian manifold, especially those of a Sasakian space form. §2 is devoted to the study of contact CR-submanifolds with nonvanishing parallel mean curvature vector and parallel f-structure in the normal bundle immersed in a Sasakian space form. Moreover, we suppose that the second fundamental...
Contact CR-warped product submanifolds in generalized Sasakian space forms.
Contact normal submanifolds and contact generic normal submanifolds in Kenmotsu manifolds.
We study contact normal submanifolds and contact generic normal in Kenmotsu manifolds and in Kenmotsu space forms. Submanifolds mentioned above with certain conditions in forms space Kenmotsu are shown that they CR-manifolds, spaces of constant curvature, locally symmetric and Einsteinnian. Also, the non-existence of totally umbilical submanifolds in a Kenmotsu space form -1 is proven under a certain condition.
Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature.
Convex Immersions of Closed Surfaces in E3.
Courbures et basculements des sous-variétés riemanniennes
CR structures on real hypersurfaces of a complex projective space.
CR submanifolds of maximal CR dimension in complex manifolds
The aim of this paper is to investigate n-dimensional real submanifolds of complex manifolds in the case when the maximal holomorphic tangent space is (n-1)-dimensional. In particular, we give some examples and we consider the Levi form on these submanifolds, especially when the ambient space is a complex space form. Moreover, we show that on some remarkable class of real hypersurfaces of complex space forms, the Levi form cannot vanish identically.