Tensor-invariants of submanifolds
The Classification of Hypersurfaces of a Euclidean Space with Parallel Higher Order Fundamental Form.
The cubic representation of a submanifold.
The Fundamental Equations of Minimal Surfaces in C2.
The Induced Connections on the Subspaces in Miron's Osckm
The induced TMA-connections of a Finslerian hypersurface
The mean curvature of the second fundamental form of a hypersurface.
The Segre imbedding and its converse
The semiring of immersions of manifolds.
The spread of the shape operator as conformal invariant.
Theory of semisymmetric conformally flat and biharmonic submanifolds.
Totally real submanifolds of a complex space form.
Totally real surfaces in with parallel mean curvature vector.
Totally Umbilical Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold
2000 Mathematics Subject Classification: 53C40, 53B25.In the present note we study totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold. We have obtained a classification theorem for totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold.
Totally umbilical submanifolds in some semi-Riemannian manifolds
We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.
Traceless cubic forms on statistical manifolds and Tchebychev geometry
Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.
Translation surfaces of finite type in
In the homogeneous space Sol, a translation surface is parametrized by , where and are curves contained in coordinate planes. In this article, we study translation invariant surfaces in , which has finite type immersion.
Transversally symmetric immersions
We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.