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The isoperimetric inequality and the total absolute curvature of closed curves in spheres

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References

  1. Bernstein, F.: Über die isoperimetrische Eigenschaft des Kreises auf der Kugeloberfläche und in der Ebene. Math. Ann.60 117–136 (1905)

    Article  MathSciNet  MATH  Google Scholar 

  2. Borsuk, M.: Sur la courbure totale des courbes fermées. Ann. Soc. Pol. Math.20 251–265 (1948)

    MATH  MathSciNet  Google Scholar 

  3. Brickell, F., Hsiung, C.C.: The total absolute curvature of closed curves in Riemannian manifolds. J. Diff. Geo.9, 177–193 (1947)

    MathSciNet  Google Scholar 

  4. Burago, Yu.D., Zalgaller, V.A.: Geometric Inequalities. Berlin etc.: Springer 1988

    MATH  Google Scholar 

  5. Fary, I.: Sur la courbure totale d’une courbe gauche faisant un nœd. Bull. Soc. Math. France77, 128–138 (1949)

    MATH  MathSciNet  Google Scholar 

  6. Fenchel, W.: Über Krümmung und Windung geschlossener Raumkurven. Math. Ann.101 238–252 (1929)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fenchel, W.: On the differential geometry of closed space curves. Bull. Amer. Math. Soc.57 44–54 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fox, R.H.: On the total curvature of some tame knots. Ann. of Math.52 (nr. 2) 258–260 (1950)

    Article  MathSciNet  Google Scholar 

  9. Kuiper, N.H.: A new knot invariant. Math. Ann.278 193–209 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Milnor, J.W.: On the total curvature of knots. Ann. of Math.52 (nr. 2) 248–257 (1950)

    Article  MathSciNet  Google Scholar 

  11. Milnor, J.W.: On the total curvature of closed space curves. Math. Scand.1 289–296 (1953)

    MATH  MathSciNet  Google Scholar 

  12. Reshetnyak, Yu.G.: Some applications of integral geometry of the theory of curves of finite turn. Sib. Mat. Zh.29 (no. 1)(167) 141–150 (1988)

    MATH  MathSciNet  Google Scholar 

  13. Szenthe, J.: On the total curvature of closed curves in Riemannian manifolds. Publ. Math. Debrecen15 99–105 (1968)

    MATH  MathSciNet  Google Scholar 

  14. Teufel, E.: Eine differentialtopologische Berechnung der totalen Krümmung und totalen Absolutkrümmung in der sphärischen Differentialgeometrie. manuscripta math.31 119–147 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  15. Teufel, E.: On the total absolute curvature of immersions into hyperbolic spaces. Coll. Math. Soc. J. Bolyai.46, Topics in Diff. Geo. Debrecen (Hungary) 1201–1208 (1984)

    MathSciNet  Google Scholar 

  16. Teufel, E.: On the total absolute curvature of closed curves in spheres. manuscripta math.57 101–108 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  17. Teufel, E.: A Generalization of the Isoperimetric Inequality in the Hyperbolic Plane. Arch. Math.57 508–513 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  18. Totaro, B.: Space curves with non-zero torsion. Internat. J. of Mathematics1 (no. 1) 109–117 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  19. Tsukamoto, Y.: On the total absolute curvature of closed curves in manifolds of negative curvature. Math. Ann.210, 313–319 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  20. Voss, K.: Eine Bemerkung über die Totalkrümmung geschlossener Raumkurven. Arch. Math.6 259–263 (1955)

    Article  MATH  MathSciNet  Google Scholar 

  21. Wintgen, P.: On the total absolute curvature of nonclosed submanifolds. Ann. Glob. Analysis and Geometry2 (No. 1) 55–87 (1984)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut B, Universität Stuttgart, Pfaffenwaldring 57, D-7000, Stuttgart 80, Federal Republic of Germany

    Eberhard Teufel

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  1. Eberhard Teufel
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Dedicated to K. Leichtweiß on his 65th birthday

This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990

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Teufel, E. The isoperimetric inequality and the total absolute curvature of closed curves in spheres. Manuscripta Math 75, 43–48 (1992). https://doi.org/10.1007/BF02567070

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  • DOI: https://doi.org/10.1007/BF02567070

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