Výsledky vyhledávání - "Mendonça, Sérgio"

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Generalizing axioms of $r$-planes and $r$-spheres on Riemannian and K\'ahler manifolds

Autor: Levina, Cristina, Mendonça, Sérgio

The famous theorems of Cartan, related to the axiom of $r$-planes, and Leung-Nomizu about the axiom of $r$-spheres were extended to K\"ahler geometry by several authors. In this paper we replace the strong notions of totally geodesic submanifolds ($r

Externí odkaz: http://arxiv.org/abs/1511.08751

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Splitting, parallel gradient and Bakry-Emery Ricci curvature

Autor: Mendonça, Sérgio

In this paper we obtain a splitting theorem for the symmetric diffusion operator $\Delta_\phi=\Delta-\left<\nabla\phi,\nabla \right>$ and a non-constant $C^3$ function $f$ in a complete Riemannian manifold $M$, under the assumptions that the Ricci cu

Externí odkaz: http://arxiv.org/abs/1502.00185

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Complete negatively curved immersed ends in $\Bbb R^3$

Autor: Mendonça, Sérgio

This paper extends, in a sharp way, the famous Efimov's Theorem to immersed ends in $\real^3$. More precisely, let $M$ be a non-compact connected surface with compact boundary. Then there is no complete isometric immersion of $M$ into $\Bbb R^3$ sati

Externí odkaz: http://arxiv.org/abs/1405.1280

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Isometry actions and geodesics orthogonal to submanifolds

Autor: Di Scala, Antonio J., Mendonça, Sérgio, Mirandola, Heudson, Ruiz-Hernández, Gabriel

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 horospheres in Hadamard manifolds.
Comment: 16 pages

Externí odkaz: http://arxiv.org/abs/1210.0527

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Homotopy Groups, Focal Points and Totally Geodesic Immersions

Autor: Mendonça, Sérgio, Mirandola, Heudson

In this paper we consider on a complete Riemannian manifold $M$ an immersed totally geodesic hypersurface $\Si$ existing together with an immersed submanifold $N$ without focal points. No curvature condition is needed. We obtained several connectedne

Externí odkaz: http://arxiv.org/abs/1108.1822

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