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Journal of the London Mathematical Society Advance Access published online on May 3, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm012
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© 2007 London Mathematical Society

Total absolute curvature and tight submanifolds in hyperbolic space

Gil Solanes

Departament d'Àlgebra i Geometria
Universitat de Barcelona
Gran Via de les Corts Catalanes 585
08007 Barcelona
Spain
solanes{at}ub.edu

An integral-geometric formula for the total absolute curvature of tight submanifolds in hyperbolic space is given. Counterexamples to the Chern–Lashof inequality are constructed in hyperbolic space of dimension 3.

2000 Mathematics Subject Classification 53C42, 53A35, 53C65.

Work partially supported by MCYT-FEDER Grant No. BMF2003-03458.

Received April 7, 2006;
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