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manuscripta mathematica

, Volume 39, Issue 2–3, pp 201–218 | Cite as

Total curvature of manifolds in self-immersed manifolds

  • Toru Ishihara
Article
  • 26 Downloads

Abstract

Chern-Lashof [3] and Kuiper [5] showed the total absolute curvature of a manifold in Euclidean space equals the mean value of the number of critical points of height functions. Teufel [10] proved that a similar result holds for the total absolute curvature of a manifold in a unit sphere. The purpose of this paper is to extend Teufel's result to a relation between the total absolute curvature of some manifolds in self-immersed manifolds and the mean value of the number of zeros of certain vector fields.

Keywords

Vector Field Fundamental Form Measure Zero Local Coordinate System Height Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Toru Ishihara
    • 1
  1. 1.Mathematical Department of Tokushima UniversityTokushimaJapan

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