Displaying similar documents to “Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4 Пълна интегруемост на една нелинейна елиптична система, пораждаща би-омбилични фолирани полусиметрични хиперповърхнини в R^4”

On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)

Commentationes Mathematicae Universitatis Carolinae

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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...

Real hypersurfaces in complex space forms concerned with the local symmetry

Seon Mi Lyu, Juan de Dios Pérez, Young Jin Suh (2007)

Czechoslovak Mathematical Journal

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This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface M in complex space form M m ( 4 ϵ ) . In the second, we give a complete classification of real hypersurfaces in M m ( 4 ϵ ) which satisfy the above geometric facts.