The isometry groups of manifolds admitting nonconstant convex functions

Robert E. GREENE; Katsuhiro SHIOHAMA

doi:10.2969/jmsj/03910001

Robert E. GREENE, Katsuhiro SHIOHAMA

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ジャーナルフリー

1987 年 39 巻 1 号 p. 1-16

DOI https://doi.org/10.2969/jmsj/03910001

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Published: 1987 Received: 1985/06/07 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: 引用文献情報訂正内容: Wrong : 1) S. Alexander and R. Bishop, Convex supporting domains on spheres, Illinois J. Math., 18 (1974), 34-47.
2) V. Bangert, Totally convex sets in complete Riemannian manifolds, J. Duff. Geom., 18 (1981), 333-345.
3) H. Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary dimension, Bull. Amer. Math. Soc., 76 (1970), 767-771.
4) R. E. Greene and K. Shiohama, Convex functions on complete noncompact manifolds: Topological structure, Invent. Math., 63 (1981), 129-157.
5) R. E. Greene and K. Shiohama, Convex functions on complete noncompact manifolds: Differentiable structure, Ann. Sci. École Norm. Sup. (4), 14 (1981), 357-367.
6) S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience, New York, 1963.
7) W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
8) T. Yamaguchi, The isometry groups of Riemannian manifolds admitting strictly convex functions, Ann. Sci. École Norm. Sup. (4), 15 (1982), 205-212.

Right : [1] S. Alexander and R. Bishop, Convex supporting domains on spheres, Illinois J. Math., 18 (1974), 34-47.
[2] V. Bangert, Totally convex sets in complete Riemannian manifolds, J. Diff. Geom., 18 (1981), 333-345.
[3] H. Federer, The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary dimension, Bull. Amer. Math. Soc., 76 (1970), 767-771.
[4] R. E. Greene and K. Shiohama, Convex functions on complete noncompact manifolds: Topological structure, Invent. Math., 63 (1981), 129-157.
[5] R. E. Greene and K. Shiohama, Convex functions on complete noncompact manifolds: Differentiable structure, Ann. Sci. École Norm. Sup. (4), 14 (1981), 357-367.
[6] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience, New York, 1963.
[7] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
[8] T. Yamaguchi, The isometry groups of Riemannian manifolds admitting strictly convex functions, Ann. Sci. École Norm. Sup. (4), 15 (1982), 205-212.

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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