Geodesic
ON SUBMANIFOLDS WITH TAMED SECOND FUNDAMENTAL FORM
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 669-680

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DOI

Based on the ideas of Bessa, Jorge and Montenegro (Comm. Anal. Geom., vol. 15, no. 4, 2007, pp. 725–732) we show that a complete submanifold M with tamed second fundamental form in a complete Riemannian manifold N with sectional curvature KN ≤ κ ≤ 0 is 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 realised as submanifold with tamed second fundamental form of a Hadamard manifold with sectional curvature bounded below. 
BESSA, G. PACELLI; COSTA, M. SILVANA. ON SUBMANIFOLDS WITH TAMED SECOND FUNDAMENTAL FORM. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 669-680. doi: 10.1017/S0017089509990085
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     title = {ON {SUBMANIFOLDS} {WITH} {TAMED} {SECOND} {FUNDAMENTAL} {FORM}},
     journal = {Glasgow mathematical journal},
     pages = {669--680},
     year = {2009},
     volume = {51},
     number = {3},
     doi = {10.1017/S0017089509990085},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990085/}
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