Acta Mathematica Hungarica

, Volume 76, Issue 3, pp 249–256 | Cite as

On the Definition of Total Absolute Curvatures in Integral Geometry

  • X. Gual Arnau


Integral Geometry Absolute Curvature Total Absolute Curvature 
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  1. [1]
    A. J. Baddeley, Absolute curvatures in integral geometry, Math. Proc. Camb. Phil. Soc., 88 (1980), 45–58.Google Scholar
  2. [2]
    S. S. Chern and K. Lashof, On the total curvature of immersed manifolds I, Amer. J. Math., 79 (1957), 246–258.Google Scholar
  3. [3]
    S. S. Chern and K. Lashof, On the total curvature of immersed manifolds II, Michigan Math. Jour., 5 (1958), 5–12.Google Scholar
  4. [4]
    H. Federer, Geometric Measure Theory, Springer Verlag (Berlín, 1969).Google Scholar
  5. [5]
    M. Golubitsky and V. Guillemin, Stable Mappings and their Singularities, Springer-Verlag (New York, 1973).Google Scholar
  6. [6]
    X. Gual, Measure of linear spaces and total curvatures of compact anti-invariant submanifolds in Cn, in: Proc. Differential Geometry and its Applications (1992). Silesian University at Opava, Czech Republic Ed.: O. Kowalski and D. Krupka (1993), pp. 13–22.Google Scholar
  7. [7]
    X. Gual and A. M. Naveira, Total curvatures of compact complex submanifolds in CP n, Annals of Global Analysis and Geometry, 13 (1995), 9–18.Google Scholar
  8. [8]
    R. Langevin and T. Shifrin, Polar varieties and integral geometry, Amer. J. Math., 104 (1980), 553–605.Google Scholar
  9. [9]
    T. Otsuki, On the total curvature of surfaces in Euclidean space, Japan J. M. Math., 35 (1966), 61–71.Google Scholar
  10. [10]
    L. A. Santaló, Curvaturas absolutas totales de varicades contenidas en un espacio euclideano, Acta Ci. Compostelana., 5 (1969), 149–158.Google Scholar
  11. [11]
    L. A. Santaló, Mean values and curvatures, Izv. Akad. Nauk. Armjan SSR, Sr.mat., 5 (1970), 286–295.Google Scholar
  12. [12]
    L. A. Santaló, Total curvatures of compact manifolds immersed in euclidean space, Simp. Mat. Ist. Naz. Alta Mat. Roma, 14 (1974), 364–390.Google Scholar
  13. [13]
    T. J. Willmore, Tight immersions and total absolute curvature, Bull. London Math. Soc., 3 (1971), 129–151.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • X. Gual Arnau
    • 1
  1. 1.Departament de MatemàtiquesCampus Penyeta Roja Universitat Jaume ICastellónSpain

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