On submanifolds with tamed second fundamental form

Details On submanifolds with tamed second fundamental form On submanifolds with tamed second fundamental form

2008-05-02

arxiv.org/abs/0805.0323v1

Glasg. Math. J. 51 (2009), no. 3, 669--680.

Mathematics

Differential Geometry

10 pages

Scientific paper

10.1017/S0017089509990085

We show that a complete submanifold $M$ with tamed second fundamental form in a complete Riemannian manifold $N$ with sectional curvature $K_{N}\leq \kappa \leq 0$ 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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