Chen inequalities for submanifolds of a locally conformal almost cosymplectic manifold with a semi-symmetric metric connection.
Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds
Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen-Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost...
Chen's inequality in the Lagrangian case
In the theory of submanifolds, the following problem is fundamental: establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities. To analyze such problems, we follow the idea of C. Udrişte that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequality which characterizes a totally real submanifold of a complex space form....
Circles and spheres in pseudo-Riemannian geometry.
Classification of homogeneous submanifolds in homogeneous spaces.
Clifford hypersurfaces in a unit sphere.
Cliffordalgebren und neue isoparametrische Hyperflächen.
Closed hypersurfaces of with two constant symmetric curvatures
Cohomology of CR-submanifolds
Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms
In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results...
Compact Einstein Kähler submanifolds of a complex projective space.
Compact hypersurfaces with constant higher order mean curvatures.
A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature Hr, for some r = 1, ..., n.
Compact space-like hypersurfaces in de Sitter space.
Compact space-like submanifolds with parallel mean curvature vector of a pseudo-Riemannian space
Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms
Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian...
Complete Hypersurfaces in the Space Form with Three Principal Curvatures.
Complete Hypersurfaces of R4 with Constant Mean Curvature.
Complete lifts of harmonic maps and morphisms between Euclidean spaces.
Complete noncompact submanifolds with flat normal bundle
Let Mⁿ (n ≥ 3) be an n-dimensional complete super stable minimal submanifold in with flat normal bundle. We prove that if the second fundamental form A of M satisfies , where α ∈ [2(1 - √(2/n)), 2(1 + √(2/n))], then M is an affine n-dimensional plane. In particular, if n ≤ 8 and , d = 1,3, then M is an affine n-dimensional plane. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite -norm curvature in ℝ⁷ are considered.
Complete real Kähler Euclidean hypersurfaces are cylinders
In this note we show that any complete Kähler (immersed) Euclidean hypersurface must be the product of a surface in with an Euclidean factor .