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On the Volume in Homogeneous Spaces

Published online by Cambridge University Press:  22 January 2016

Minoru Kurita
Minoru Kurita*
Affiliation:
Mathematical Institute Nagoya University
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Guldin-Pappus’s theorem about the volume of a solid of rotation in the euclidean space has been generalized in two ways. G. Koenigs [1] and J. Hadamard [2] proved that the volume generated by a 1-parametric motion of a surface D bounded by a closed curve c is equal to where are quantities attached to D with respect to a rectangular coordinate system, while are quantities determined by our motion.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 15 , August 1959 , pp. 201 - 217
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1959

References

[13] Koenigs, G., Sur la détermination générale du volume engendré par un contour fermégauche ou plan dans un mouvement quelconque, Jour, de Math. 1889.Google Scholar
[2] Hadamard, J., Sur la généralization du théorème de Guldin, Bull, des Sc. Math. t. 26, 1898.Google Scholar
[3] Bloch, A. and Guillaumin, G., La géométrie integrale du contour gauche, Gauthier Villars, 1949.Google Scholar
[4] Cartan, E., La théorie des groupes finis et contunus et la géométrie différentielle par la methode du reperes mobiles, Gauthier Villars, 1938.Google Scholar
[5] Blaschke, W., Integralgeometrie, Actualites scientifiques et industrielles, 1935.Google Scholar
[6] Kurita, M., On the vector in homogeneous spaces, Nagoya Math. Jour. vol. 5, 1953.Google Scholar
[7] Kurita, M., On some formulas about volume and surface area, Nagoya Math. Jour. vol. 6, 1954.Google Scholar