Two results in the affine hypersurface theory

Takashi KUROSE

doi:10.2969/jmsj/04130539

Takashi KUROSE

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 3 Pages 539-548

DOI https://doi.org/10.2969/jmsj/04130539

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Published: 1989 Received: April 04, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Two results in the affine hypereurface theory
Right : Two results in the affine hypersurface theory

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer, 1923.
2) E. Calabi, Complete affine hypersphere I, Sympos. Math., 10 (1972), 19-38.
3) S. Y Cheng and S. T. Yau, On the regularity of the solution of the n-dimensional Minkowski problem, Comm Pure Appl. Math., 29 (1976), 495-516.
4) S. Y Cheng and S. T. Yau, Complete affine hypersurfaces, Part I The completeness of affine metrics, Comm. Pure Appl. Math., 39 (1986), 839-866.
5) H. Flanders, Local theory of affine hypersurfaces, J. Analyse Math., 15 (1965), 353-387.
6) H. Guggenheimer, Differential Geometry, McGraw-Hill, 1963.
7) K. Nomizu and U. Pinkall, On the geometry of affine immersions, Math. Z., 195 (1987), 165-178.
8) A. V. Pogorelov, The Minkowski Multidimensional Problem, V. H. Winston & Sons, 1978.
9) T. Sasaki, Hyperbolic affine hyperspheres, Nagoya Math J., 77 (1980), 107-123.

Right : [1] W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer, 1923.
[2] E. Calabi, Complete affine hypersphere I, Sympos. Math., 10 (1972), 19-38.
[3] S. Y Cheng and S. T. Yau, On the regularity of the solution of the n-dimensional Minkowski problem, Comm Pure Appl. Math., 29 (1976), 495-516.
[4] S. Y Cheng and S. T. Yau, Complete affine hypersurfaces, Part I The completeness of affine metrics, Comm. Pure Appl. Math., 39 (1986), 839-866.
[5] H. Flanders, Local theory of affine hypersurfaces, J. Analyse Math., 15 (1965), 353-387.
[6] H. Guggenheimer, Differential Geometry, McGraw-Hill, 1963.
[7] K. Nomizu and U. Pinkall, On the geometry of affine immersions, Math. Z., 195 (1987), 165-178.
[8] A. V. Pogorelov, The Minkowski Multidimensional Problem, V. H. Winston & Sons, 1978.
[9] T. Sasaki, Hyperbolic affine hyperspheres, Nagoya Math J., 77 (1980), 107-123.

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