On Submanifolds with Tamed Second Fundamental Form

نویسنده

  • SILVANA COSTA
چکیده

Based on the ideas of Bessa-Jorge-Montenegro [4] we show that a complete submanifold M with tamed second fundamental form in a complete Riemannian manifold N with sectional curvature KN ≤ κ ≤ 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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تاریخ انتشار 2008