ON ALMOST STABLE CMC HYPERSURFACES IN MANIFOLDS OF BOUNDED SECTIONAL CURVATURE

We show that almost stable constant mean curvature hypersurfaces contained in a sufficiently small ball of a manifold of bounded sectional curvature are close to geodesic spheres.

CHARACTERIZATIONS OF BERGER SPHERES FROM THE VIEWPOINT OF SUBMANIFOLD THEORY

In this paper, Berger spheres are regarded as geodesic spheres with sufficiently big radii in a complex projective space. We characterize such real hypersurfaces by investigating their geodesics and contact structures from the viewpoint of submanifold theory.

Ruled three-dimensional CR submanifolds of the sphere S6(1)

We investigate proper, three-dimensional CR submanifolds of the nearly Kahler sphere S6(1) ruled by totally geodesic spheres S2(1), and classify them by using a sphere curve and a vector field along that curve.

A NEW RESULT ABOUT ALMOST UMBILICAL HYPERSURFACES OF REAL SPACE FORMS

In this short note, we prove that an almost umbilical compact hypersurface of a real space form with almost Codazzi umbilicity tensor is embedded, diffeomorphic and quasi-isometric to a round sphere. Then, we derive a new characterisation of geodesic spheres in space forms.