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Tightness of manifolds with $H$-spherical ends

Published online by Cambridge University Press:  04 December 2007

MARTIN VAN GEMMEREN
MARTIN VAN GEMMEREN
Affiliation:
Mathematisches Institut B Universität Stuttgart 70550 Stuttgart Germany. e-mail: mvg@mathematik.uni-stuttgart.de
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Abstract

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In this article we prove a Chern–Lashof inequality for immersions of manifolds with H-spherical ends. Related to this inequality we discuss different types of tightness. In particular we shall prove that an immersion of a manifold with at least two H-spherical ends is tightly immersed only if the ends are of a certain geometric type (Wintgen immersion).

Keywords

Chern-Lashof inequalityMorse number$H$-spherical endsstrongweak and total tightness.
Type
Research Article
Information
Compositio Mathematica , Volume 112 , Issue 1 , May 1998 , pp. 17 - 32
Copyright
© 1998 Kluwer Academic Publishers