Dept. Math, Hokkaido Univ. EPrints Server

HORO-TIGHT IMMERSIONS OF S^1

Preprint Series # 711
Buosi, Marcelo and Izumiya, Shyuichi and Soares Ruas, Mria Aoarecida HORO-TIGHT IMMERSIONS OF S^1. (2005);

[img]PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
174Kb

Abstract

We characterize horo-tight immersions into $\D^m$ in terms of a family of real valued functions parametrized by $\Ss^{m-1}$. By means of such functions we provide an elementary proof that horo-tightness and tightness are equivalent properties in the class of immersions from $S^1$ into hyperbolic space.

Item Type:Preprint
Additional Information:50\bibitem{CW70}{S. Carter and A. West}, {\em Tight ant taut immersions}, Proc. London Math. Soc, (3) {\bf 25} (1972), 701-720. \bibitem{C74}{T. E. Cecil}, {\em A characterization of metric spheres in hyperbolic space by Morse theory}, Toh\^oku Math. J., {\bf 26} (1974), 341-351. \bibitem{CR79I}{T. E. Cecil and P. J. Ryan}, {\em Distance functions and umbilic submanifolds of hyperbolic space}, Nagoya Math. J., {\bf 74} (1979), 67-75. \bibitem{CR79}{T. E. Cecil and P. J. Ryan}, {\em Tight ant taut immersions into hyperbolic space}, J. London Math. Soc., {\bf 19} (1979), 561-572. \bibitem{CR85}{T. E. Cecil and P. J. Ryan}, {\em Tight ant taut immersions of manifolds}, Research Notes in Mathematics, {\bf 107} (1985). \bibitem{RGR94}{R. G. Ratcliffe}, {\em Foundations of hyperbolic manifolds}, Graduate Texts in Math., {\bf 149} (1994).
Uncontrolled Keywords:horo-tight immersion, tight immersion, hyperbolic space
Subjects:53-xx DIFFERENTIAL GEOMETRY
ID Code:896