The axiom of n-planes and convexity in Riemannian manifolds Dedicated to Professor I. Mogi on his 60th birthday

Nobuhiro INNAMI

doi:10.2969/jmsj/03510085

The axiom of n-planes and convexity in Riemannian manifolds

Dedicated to Professor I. Mogi on his 60th birthday

Nobuhiro INNAMI

著者情報

ジャーナルフリー

1983 年 35 巻 1 号 p. 85-91

DOI https://doi.org/10.2969/jmsj/03510085

詳細

Published: 1983 Received: 1981/04/16 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Nobuhiro TNNAMI¹⁾
Right : Nobuhiro INNAMI¹⁾

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) E. Beltrami, Teoria fondamentale degli spazii di curvatura costante, Annali di Matem., (2) 2 (1868-69), 232-255.
2) H. Busemann, The Geometry of geodesics, Academic Press, New York, 1955.
3) É. Cartan, L'axiome du plan et la géométrie différentielle metrique, Euvres complètes, Partie III, 2, Gauthier-Villars, Paris, 1955.
4) É. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1928.
5) J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math., 96 (1972), 413-443.
6) D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Math., 55, Springer, Berlin-Heidelberg-New York, 1968.
7) S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978.
8) W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, New Jersey, 1948.
9) F. Klein, Ueber die sogenannte nicht-euklidische Geometrie, Math. Ann., 6 (1873), 112-145.
10) D. S. Leung and K. Nomizu, The axiom of spheres in Riemannian geometry, J. Differential Geometry, 5 (1971), 487-489.
11) L. Schlaefli, Nota alla Memoria del sig. Beltrami, (Sugli spazii di curvatura costante), Annali di Matem., (2) 5, (1871-73).
12) F. Schur, Ueber den Zusammenhang der Räume constanten Riemann'schen Krümmungsmasses mit den projectiven Räumen, Math. Ann., 27 (1886), 537-567.

Right : [1] E. Beltrami, Teoria fondamentale degli spazii di curvatura costante, Annali di Matem., (2) 2 (1868-69), 232-255.
[2] H. Busemann, The Geometry of geodesics, Academic Press, New York, 1955.
[3] É. Cartan, L'axiome du plan et la géométrie différentielle metrique, Œuvres complètes, Partie III, 2, Gauthier-Villars, Paris, 1955.
[4] É. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1928.
[5] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math., 96 (1972), 413-443.
[6] D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Math., 55, Springer, Berlin-Heidelberg-New York, 1968.
[7] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978.
[8] W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, New Jersey, 1948.
[9] F. Klein, Ueber die sogenannte nicht-euklidische Geometrie, Math. Ann., 6 (1873), 112-145.
[10] D. S. Leung and K. Nomizu, The axiom of spheres in Riemannian geometry, J. Differential Geometry, 5 (1971), 487-489.
[11] L. Schlaefli, Nota alla Memoria del sig. Beltrami, (Sugli spazii di curvatura costante), Annali di Matem., (2) 5, (1871-73).
[12] F. Schur, Ueber den Zusammenhang der Räume constanten Riemann'schen Krümmungsmasses mit den projectiven Räumen, Math. Ann., 27 (1886), 537-567.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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