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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Total absolute curvature and tightness of noncompact manifolds

Author: Martin van Gemmeren
Journal: Trans. Amer. Math. Soc. 348 (1996), 2413-2426
MSC (1991): Primary 53C42; Secondary 57R45
MathSciNet review: 1355077
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Abstract: In the first part we prove an extension of the Chern-Lashof inequality for noncompact immersed manifolds with finitely many ends. For this we give a lower bound of the total absolute curvature in terms of topological invariants of the manifold. In the second part we discuss tightness properties for such immersions. Finally, we give an upper bound for the substantial codimension.

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Martin van Gemmeren
Affiliation: Mathematisches Institut B, Universität Stuttgart, 70550 Stuttgart, Germany

Keywords: Chern-Lashof inequality, Morse number, ends of manifolds, strong and weak tightness, proper immersion, limit direction
Received by editor(s): March 8, 1995
Additional Notes: The author acknowledges support by a fellowship of the Studienstiftung des deutschen Volkes.
Article copyright: © Copyright 1996 American Mathematical Society