4 papers
Totally Umbilical Hypersurfaces of Product Spaces
Ronaldo F. de Lima, João Paulo dos Santos
Given a Riemannian manifold and an open interval we characterize nontrivial totally umbilical hypersurfaces of the product -- as well as of w…
Hypersurfaces of Product Spaces with a Canonical Direction
Ronaldo F. de Lima, Pedro Roitman
Consider a complete Riemannian manifold and let be an orientable hypersurface of the product manifold endowed with its standard product metric $\lan…
The -dimensional Peano Curve
Jaquim E. DE Freitas, Ronaldo F. de Lima, Daniel T. dos Santos
One of the most startling mathematical discoveries of the nineteen century was the existence of plane-filling curves. As is well known, the first example of such a curve was given…
Embeddedness, Convexity, and Rigidity of Hypersurfaces in Product Spaces
Ronaldo Freire de Lima
We establish the following Hadamard--Stoker type theorem: Let be a complete connected hypersurface with positive definite second fund…