4 papers
Generalizing axioms of -planes and -spheres on Riemannian and Kähler manifolds
Cristina Levina, Sérgio Mendonça
The famous theorems of Cartan, related to the axiom of -planes, and Leung-Nomizu about the axiom of -spheres were extended to Kähler geometry by several authors. In this pape…
Isometry actions and geodesics orthogonal to submanifolds
Antonio J. Di Scala, Sérgio Mendonça, Heudson Mirandola +1
We investigate submanifolds in space forms such that every geodesic orthogonal to the submanifold intersects a fixed totally geodesic submanifold. We obtain an application to horos…
Homotopy Groups, Focal Points and Totally Geodesic Immersions
Sérgio Mendonça, Heudson Mirandola
In this paper we consider on a complete Riemannian manifold an immersed totally geodesic hypersurface $\Si$ existing together with an immersed submanifold without focal poi…
Knots in Riemannian manifolds
Fuquan Fang, S. Mendonca
In this paper we study submanifold with nonpositive extrinsic curvature in a positively curved manifold. Among other things we prove that, if is a totally geode…