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The kinematic formula in integral geometry for cylinders

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Summary

We generalize the kinematic formula of Chern-Federer (1.2) to the case in which the moving manifold Ma is a cylinder in En. These cylinders and the corresponding kinematic density are suitable defined and some particular cases are considered in detail.

References

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    S. S. Chern,On the kinematic formula in Integral Geometry, J. Math. and Mech.,16 (1966), pp. 101–118.

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    H. Hadwiger,Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer, Berlin, 1957.

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    L. A. Santaló,Geometria Integral en espacios de curvatura constante, Publ. Com. Nac. Energia Atòmica, Serie Mat., vol. 1, No. 1, Buenos Aires, 1952.

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    L. A. Santaló,Sur la mesure des éspaces linéaires qui coupent un corps convexe et problemes qui s'y rattachent, Colloque sur les questions de réalité en Géometrie, Liege, 1955, pp. 177–190.

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    H. Weyl,On the volume of tubes, Amer. J. Math.,61 (1939), pp. 461–472.

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Additional information

Dedicated to ProfessorBeniamino Segre on the occasion of his 70-th birthday

Entrata in Redazione il 22 maggio 1973.

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Santaló, L.A. The kinematic formula in integral geometry for cylinders. Annali di Matematica 103, 71–79 (1975) doi:10.1007/BF02414144

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Keywords

  • Integral Geometry
  • Kinematic Formula
  • Kinematic Density