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Remarks on an inequality involving the normal scalar curvature
We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature. We translate it into an algebraic problem,Expand
A complete classification of parallel surfaces in three-dimensional homogeneous spaces
We complete the classification of surfaces with parallel second fundamental form in all three-dimensional homogeneous spaces.
ON EXTRINSICALLY SYMMETRIC HYPERSURFACES OF ℍ n ×ℝ
Totally umbilical, semi-parallel and parallel hypersurfaces of ℍ n ×ℝ are completely classified. More examples arise than in the analogous study on the ambient space 𝕊 n ×ℝ.
LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES
We describe a global model for Lorentzian symmetric three-spaces admitting a parallel null vector field, and classify completely the surfaces with parallel second fundamental form in all LorentzianExpand
Parallel surfaces in Lorentzian three-manifolds admitting a parallel null vector field
We classify parallel surfaces in Lorentzian three-manifolds admitting a parallel null vector field. Some families of semi-parallel surfaces are also described.
Rotation hypersurfaces in and
We introduce the notion of rotation hypersurfaces of and and we prove a criterium for a hypersurface ofone of these spaces to be a rotation hypersurface. Moreover, weclassify minimal rotationExpand
Classification of constant angle surfaces in a warped product
Let I µ R be an open interval, f : I ! R a strictly positive function and denote by E 2 the Euclidean plane. We classify all surfaces in the warped product manifold I £f E 2 for which the unit normalExpand
Spatial and Lorentzian surfaces in Robertson-Walker space times
Let L14(f,c)=(I×fS,gfc) be a Robertson-Walker space time which does not contain any open subset of constant curvature. In this paper, we provide a general study of nondegenerate surfaces in L14(f,c).Expand
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