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ON SUBMANIFOLDS WITH TAMED SECOND FUNDAMENTAL FORM

Published online by Cambridge University Press:  01 September 2009

G. PACELLI BESSA  and
M. SILVANA COSTA
G. PACELLI BESSA
Affiliation:
Universidade Federal do Ceara, Brazil e-mail: gpbessa@yahoo.com.br
M. SILVANA COSTA
Affiliation:
Universidade Federal do Ceara, Brazil e-mail: silvana_math@yahoo.com.br
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 669 - 680
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

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