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Fenchel type theorems for submanifolds of Sn

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Commentarii Mathematici Helvetici

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References

  • [Ba]T. Banchoff,Total central curvature of curves, Duke Math. Journal37 (1970), 281–289.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ch]S. S. Chern,On the kinematic formula in integral geometry, Math. and Mechanica16 (1966), 101–118.

    MathSciNet  MATH  Google Scholar 

  • [C-L]S. S. Chern andR. K. Lashoff,On the total curvature of immersed manifolds, II, Mich. Math. Journ.5 (1958), 5–12.

    Article  MATH  Google Scholar 

  • [Fa]I. Fary,Sur la courbure totale d'une courbe gauche faisant un noeud, Bull. S.M.F.78 (1949), 128–138.

    MathSciNet  Google Scholar 

  • [Fe]M. Fenchel,On total curvature of Riemannian manifolds I, Journ. Lond. Math. Soc.15 (1940), 15–22.

    MathSciNet  MATH  Google Scholar 

  • [J-L]C. Jacobi andR. Langevin,Habitat geometry of marine benthic substrates: effect on early stages of colonization, Journal of Experimental Marine Biology, and Ecology, to appear.

  • [K-M]N. Kuiper andW. Meeks,Total curvature of knotted surfaces, Invent.77 (1984), 25–69.

    Article  MathSciNet  MATH  Google Scholar 

  • [L]R. Langevin,Classe moyenne d'une sous-variété d'une sphère ou d'un espace projectif, Rend. Circ. Mat. di Palermo, serie 2, tomo28 (1979), 313–318.

    MathSciNet  MATH  Google Scholar 

  • [L-S]R. Langevin andT. Shifrin,Polar varieties and integral geometry, Amer. Journ. math.104 (1982), 553–605.

    Article  MathSciNet  MATH  Google Scholar 

  • [L-R]R. Langevin andH. Rosenberg, On total curvature and knots, Topol.15 (1976), 405–416.

    Article  MathSciNet  MATH  Google Scholar 

  • [M1]J. Milnor,On the total curvature of knots, Annals Math.52 (1949), 248–260.

    Article  MathSciNet  Google Scholar 

  • [M2]J. Milnor,On the total curvature of closed space curves, Math. Scand.1 (1953), 289–296.

    MathSciNet  MATH  Google Scholar 

  • [Sa]L. A. Santalo,Integral geometry and geometric probability, Encyl. of Math. and its applications, Addison Wesley (1976).

  • [Sl]V. V. Slavski,Integral geometric relations with an orthogonal projection for surfaces, Sib. Math. Journ.16 (1975), 275–284.

    Article  Google Scholar 

  • [Su]D. Sunday,The total curvature of knotted spheres, Bull. Amer. Math. Soc.82 (1976), 140–142.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Topologie, Université de Bourgogne, UMR 55 84 9 ave. A. Savary, B.P. 400, 21011, Dijon Cedex, France

    Remi Langevin

  2. Université de Paris, 2, Place Jussieu, 75251, Paris, France

    Harold Rosenberg

Authors
  1. Remi Langevin
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  2. Harold Rosenberg
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We dedicate this paper to the memory of Nicolaas Kuiper

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Langevin, R., Rosenberg, H. Fenchel type theorems for submanifolds of Sn . Commentarii Mathematici Helvetici 71, 594–616 (1996). https://doi.org/10.1007/BF02566438

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  • DOI: https://doi.org/10.1007/BF02566438

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