On the existence of parallel normal vector fields of surfaces in
On the first Chern class of a complex submanifold in an almost Hermitian manifold and the normal connection
On the Focal Locus of a Submanifold in a Riemannian Manifold of Constant Sectional Curvature
On the four vertex theorem in planes with radial density
It is shown that in a plane with a radial density the four vertex theorem holds for the class of all simple closed curves if and only if the density is constant. On the other hand, for the class of simple closed curves that are invariant under a rotation about the origin, the four vertex theorem holds for every radial density.
On the geometry of a partial product structure
On the -theorem for hypersurfaces
On the Higher Mean Curvature Functions of Kaehler Hypersurfaces in Complex Space Forms.
On the invariant method in differential geometry of submanifolds
On the Kenmotsu hypersurfaces of special Hermitian manifolds.
On the Nonexistence of a Hypersurface of Prescribed Mean Curvature with a Given Boundary.
On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture
Let M̅ be a compact Riemannian manifold with sectional curvature satisfying (resp. ), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in M̅. This extends Shen and Xu’s result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.
On the normality of an almost contact -structure on -submanifolds
We study -dimensional -submanifolds of -dimension immersed in a quaternionic space form , , and, in particular, determine such submanifolds with the induced normal almost contact -structure.
On the problem whether the image of a given differentiable map into Riemannian manifold is contained in a submanifold with parallel second fundamental form.
On the rigidity of certain surfaces in
On the role of partial Ricci curvature in the geometry of submanifolds and foliations
Submanifolds and foliations with restrictions on q-Ricci curvature are studied. In §1 we estimate the distance between two compact submanifolds in a space of positive q-Ricci curvature, and give applications to special classes of submanifolds and foliations: k-saddle, totally geodesic, with nonpositive extrinsic q-Ricci curvature. In §2 we generalize a lemma by T. Otsuki on asymptotic vectors of a bilinear form and then estimate from below the radius of an immersed submanifold in a simply connected...
On the structure vector field of a real hypersurface in complex two-plane Grassmannians
Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure vector field is of Jacobi type.
On the three-dimensional CR-submanifolds of the six-dimensional sphere.
On the topology of a compact submanifold of a sphere with bounded second fundamental form.
On the Topology of Riemann Spaces of Quasi-constant Curvature
On the total (non absolute) curvature of a even dimensional submanifold Xn immersed in Rn+2.
The total curvatures of the submanifolds immersed in the Euclidean space have been studied mainly by Santaló and Chern-Kuiper. In this paper we give geometrical and topological interpretation of the total (non absolute) curvatures of the even dimensional submanifolds immersed in Rn+2. This gives a generalization of two results obtained by Santaló.