Non-rational minimal spheres and minimizing cones.
Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds
By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.
On 1-harmonic functions.
On 2-quasi-umbilical pseudosymmetric hypersurfaces in the Euclidean space.
On 3-dimensional CR-manifolds
On a class of minimal hypersurfaces in Rn.
On a conjecture about the Gauss map of complete spacelike surfaces with constant mean curvature in the Lorentz-Minkowski space.
On a Theorem of Fenchel-Borsuk-Willmore-Chern-Lashof.
On Asymptotic Directions of Minimal Immersions.
On complete hypersurfaces with two distinct principal curvatures in a hyperbolic space.
On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds
Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.
On complete minimal surfaces with finite Morse index in three manifolds.
On complete spacelike hypersurfaces with in locally symmetric Lorentz spaces
In this note, we investigate -dimensional spacelike hypersurfaces with in locally symmetric Lorentz space. Two rigidity theorems are obtained for these spacelike hypersurfaces.
On Conformal Minimal Immersions of S2 into CPn.
On Critical Sets of Distance Functions to a taut Submanifold.
On Deszcz symmetries of Wintgen ideal submanifolds
It was conjectured in [26] that, for all submanifolds of all real space forms , the Wintgen inequality is valid at all points of , whereby is the normalised scalar curvature of the Riemannian manifold and , respectively , are the squared mean curvature and the normalised scalar normal curvature of the submanifold in the ambient space , and this conjecture was shown there to be true whenever codimension . For a given Riemannian manifold , this inequality can be interpreted as follows:...
On Embeddings of Proper Smooth G-Manifolds.
On Equivariant Isometric Embeddings.
On foliations of ... By minimal hypersurfaces.
On Hamiltonian-minimal Lagrangian tori in .