-hypersurfaces of the six-dimensional sphere.
-totally real submanifolds of satisfying a certain inequality.
Cauchy-Riemann submanifolds of Kaehlerian Finsler spaces.
We study the geometry of the second fundamental form of a Cauchy-Riemann submanifold of a Kaehlerian Finsler space M2n; any totally-real submanifold of M2n with v-flat normal connection is shown to be a Berwald-Cartan space.
Caustics and wave front propagations: applications to differential geometry
This is mainly a survey on the theory of caustics and wave front propagations with applications to differential geometry of hypersurfaces in Euclidean space. We give a brief review of the general theory of caustics and wave front propagations, which are well-known now. We also consider a relationship between caustics and wave front propagations which might be new. Moreover, we apply this theory to differential geometry of hypersurfaces, getting new geometric properties.
Certain connections between time functions and compact spacelike submanifolds
Characteristic vector fields of generic distributions of corank 2
Characterization of a slant submanifold of a Kenmotsu manifold.
Characterization of -lightlike warped product of indefinite Kenmotsu manifolds
Characterization of totally umbilic hypersurfaces in a space form by circles
In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
Characterizations of complex space forms by means of geodesic spheres and tubes
We prove that a connected complex space form (,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition and by the semi-parallel condition , considering special choices of tangent vectors to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where , and denote the Riemann curvature tensor, the corresponding Ricci tensor of type (0,2) and the second fundamental form of the spheres or tubes and where acts as a derivation.
Characterizations of conformally flat hypersurfaces
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