On submanifolds with tamed second fundamental form

G. Pacelli Bessa; M. Silvana Costa

doi:10.1017/s0017089509990085

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arXiv · 0805.0323

On submanifolds with tamed second fundamental form

G. Pacelli Bessa·M. Silvana Costa

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Abstract

We show that a complete submanifold $M$ with tamed second fundamental form in a complete Riemannian manifold $N$ with sectional curvature $K_{N}\leq κ\leq 0$ are proper, (compact if $N$ is compact). In addition, if $N$ is Hadamard then $M$ has finite topology. We also show that the fundamental tone is an obstruction for a Riemannian manifold to be realized as submanifold with tamed second fundamental form of a Hadamard manifold with sectional curvature bounded below.

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BibTeX RIS

G. Pacelli Bessa, M. Silvana Costa. 2008-05-02. On submanifolds with tamed second fundamental form. https://doi.org/10.1017/s0017089509990085

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