Ln/2-pinching theorems for submanifolds with parallel mean curvature in a sphere

Hong-Wei XU

doi:10.2969/jmsj/04630503

L_n/2-pinching theorems for submanifolds with parallel mean curvature in a sphere

Hong-Wei XU

著者情報

ジャーナルフリー

1994 年 46 巻 3 号 p. 503-515

DOI https://doi.org/10.2969/jmsj/04630503

詳細

Published: 1994 Received: 1992/10/12 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: 論文タイトル訂正内容: Wrong : L_n/2-pinching theorems for submanifolds with parallel mean curvature in a sphere
Right : L_n/2-pinching theorems for submanifolds with parallel mean curvature in a sphere

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. Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Differential Geom., 1 (1967), 111-125.
2) B.Y. Chen, Geometry of Submanifolds, Marcel Dekker Inc., New York, 1973.
3) X.P. Chen, Harmonic mapping and Gauss mapping, Chinese Ann. Math., 4A(1983), 449-456.
4) S.S. Chern, M. do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional analysis and related fields, (ed. F.E. Browder), Springer, 1970.
5) D. Hoffman and J. Spruck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math., 27 (1974), 715-727; 28 (1975), 765-766.
6) J.M. Lin and C.Y. Xia, Global pinching theorems for even dimensional minimal submanifolds in a unit sphere, Math. Z., 201 (1989), 381-389.
7) C.K. Peng and C.L. Terng, Minimal hypersurfaces of sphere with constant scalar curvature, in Seminar of minimal submanifolds, (ed. E. Bombieri), Princeton University Press, 1983.
8) R. Schoen and S.T. Yau, Differential Geometry, Academic Press, 1988.
9) C.L. Shen, A global pinching theorem for minimal hypersurfaces in a sphere, Proc. Amer. Math. Soc., 105 (1989), 192-198.
10) J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math., 88 (1968), 62-105.
11) H.W. Xu, Some results on geometry of Riemannian submanifolds, Ph. D. dissertation, Fudan University, 1990.
12) S.T. Yau, Submanifolds with constant mean curvature I, II, Amer. J. Math., 96 (1974), 346-366; 97 (1975), 76-100.

Right : [1] E. Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Differential Geom., 1 (1967), 111-125.
[2] B. Y. Chen, Geometry of Submanifolds, Marcel Dekker Inc., New York, 1973.
[3] X. P. Chen, Harmonic mapping and Gauss mapping, Chinese Ann. Math., 4A (1983), 449-456.
[4] S. S. Chern, M. do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional analysis and related fields, (ed. F. E. Browder), Springer, 1970.
[5] D. Hoffman and J. Spruck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math., 27 (1974), 715-727; 28 (1975), 765-766.
[6] J. M. Lin and C. Y. Xia, Global pinching theorems for even dimensional minimal submanifolds in a unit sphere, Math. Z., 201 (1989), 381-389.
[7] C. K. Peng and C. L. Terng, Minimal hypersurfaces of sphere with constant scalar curvature, in Seminar of minimal submanifolds, (ed. E. Bombieri), Princeton University Press, 1983.
[8] R. Schoen and S. T. Yau, Differential Geometry, Academic Press, 1988.
[9] C. L. Shen, A global pinching theorem for minimal hypersurfaces in a sphere, Proc. Amer. Math. Soc., 105 (1989), 192-198.
[10] J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math., 88 (1968), 62-105.
[11] H. W. Xu, Some results on geometry of Riemannian submanifolds, Ph. D. dissertation, Fudan University, 1990.
[12] S. T. Yau, Submanifolds with constant mean curvature I, II, Amer. J. Math., 96 (1974), 346-366; 97 (1975), 76-100.

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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