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Generalised Umbilics on Embedded Spheres

Published online by Cambridge University Press:  20 November 2018

J. L. Noakes
J. L. Noakes*
Affiliation:
Department of Mathematics University of Western Australia Nedlands, WA 6009 Australia
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Abstract

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We study two kinds of generalized umbilics on smoothly embedded n-manifolds in ℝn+1. A sectional umbilic occurs where two of the principal curvatures are equal, and a split sectional umbilic is a more general notion.

Keywords

53A0753C40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 90 - 95
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Adams, J. F., Vector fields on spheres, Annals of Math. 75(1962) 603–632.Google Scholar
2. Bol, G., Über Nabelpunkte aufeiner Eifläche, Math. Z. 49(1944) 389–4110.Google Scholar
3. Hamburger, H., Beweis einer Caratheodoryschen Vermutung, Teil 1, Annals of Math. 41(1940) 63-86; Teil 2 Acta Math. 73 (1941), 175–228; Teil 3 Acta Math. 73(1941) 229-332.Google Scholar
4. Klotz, T., On G. Bol's proof of Carathéododory's conjecture, Comm. Pure Appl. Math. 12(1959) 277–311.Google Scholar
5. Kobayashi, S. and Nomizu, K., Foundations of differential geomety, Volume 2, Interscience, 1969.Google Scholar
6. Noakes, J. L., Lagrangian immersions and Bott periodicity, Topology and its Application 25(1987) 151– 159.Google Scholar
7. Smyth, B. and Xavier, F., Efimov's theorem in dimension greater than two, Inventiones Math. 90(1987) 443–450.Google Scholar
8. Spivak, M., A comprehensive introduction to differential geomety, Volume 3, Publish or Peirsh Inc., 1975.Google Scholar
9. Titus, C. J., A proof of a conjecture ofLoewner and of the conjecture of Caratheodory on umbilic points, Acta Mathematica 131(1973)43–77.Google Scholar