Remark on mixed foliate generic submanifolds
Remark on one theorem of R. Schneider
Remark on surfaces in satisfying certain relations between covariant derivatives of the mean and Gauss curvatures
Remark to the characterization of the sphere in
Remarks on the Stability of Minimal Submanifolds of IRn.
Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form
We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.
Ricci curvature of real hypersurfaces in complex hyperbolic space
First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.
Ricci curvature of submanifolds in Kenmotsu space forms.
Riemannian manifolds not quasi-isometric to leaves in codimension one foliations
Every open manifold of dimension greater than one has complete Riemannian metrics with bounded geometry such that is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential...
Riemannian Submersions of Compact Simple Lie Groups with Connected Totally Geodesic Fibres.
Rigidity of Rank-One Factors of Compact Symmetric Spaces
We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.
Rigidity Theorems of Hypersurfaces in a Sphere
Rotational Hypersurfaces of Space Forms with Constant scalar curvature.
Rotations and Hermitian Symmetric Spaces.