Lagrangian submanifolds of Cn with conformal Maslov form and the Whitney sphere

Antonio ROS; Francisco URBANO

doi:10.2969/jmsj/05010203

Lagrangian submanifolds of Cⁿ with conformal Maslov form and the Whitney sphere

Antonio ROS, Francisco URBANO

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ジャーナルフリー

1998 年 50 巻 1 号 p. 203-226

DOI https://doi.org/10.2969/jmsj/05010203

詳細

Published: 1998 Received: 1995/06/27 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) K. Amur and V. S. Hedge, Conformality of Riemannian manifolds to spheres J. Differential Geometry 9 (1974), 571-576.
2) A. L. Besse, Einstein Manifolds, Springer-Verlag, 1987.
3) V. Borrelli, B. Y. Chen and J. M. Morvan, A basic inequality for Lagrangian submanifolds and its application to Whitney's immersion Preprint.
4) I. Castro and F. Urbano, Lagrangian surfaces in the complex Euclidean plane with conformal Maslov form Töhoku Math. J. 45 (1993), 565-582.
5) B. Y. Chen, Geometry of Submanifolds and its Applications, Science University of Tokyo, 1981.
6) J. Erbacher, Reduction of the codimension of an isometric immersion J. Differential Geometry 5 (1971), 333-340.
7) N. Ejiri, Totally real minimal immersions of n-dimensional real space forms into n-dimendional complex space forms Proc. Amer. Math. Soc. 84 (1982), 243-246.
8) M. Gromov, Pseudo-holomorphic curves in symplectic manifolds Invent. Math. 82 (1985), 307-347.
9) J. D. Moore, Isometric immersions of Riemannian products J. Differential Geometry 5 (1971), 159-168.
10) J. M. Morvan, Classe de Maslov d'une immersion Lagrangienne et minimalite C. R. Acad. Sc. Paris 292 (1981), 633-636.
11) M. Obata, Conformal transformations of Riemannian manifolds J. Differential Geometry 4 (1970), 311-333.
12) E. A. Ruh and J. Vilms, The tension field of the Gauss map Trans. Amer. Math. Soc. 149 (1970), 569-573.
13) Y. Suyama and Y. Tsukamoto, Riemannian manifolds admitting a certain confomal transformation group J. Differential Geometry 5 (1971), 415-426.
14) S. Tanno and W. Weber, Closed conformal vector fields J. Differential Geometry 3 (1969), 361-366.
15) Y. Tashiro, Complete Riemannian manifolds and some vector fields Trans. Amer. Math. Soc. 117 (1965), 251-275.
16) F. Urbano, Totally real submanifolds Geometry and Topology of submanifolds, Worl Scientific (1989), 198-208.
17) A. Weinstein, Lectures on symplectic manifolds Conference board of the Mathematical Sciences 29 (1977).
18) S. T. Yau, Submanifolds with constant mean curvature I Amer. J. Math. 96 (1974), 346-366.

Right : [1] K. Amur and V. S. Hedge, Conformality of Riemannian manifolds to spheres J. Differential Geometry 9 (1974), 571-576.
[2] A. L. Besse, Einstein Manifolds, Springer-Verlag, 1987.
[3] V. Borrelli, B. Y. Chen and J. M. Morvan, A basic inequality for Lagrangian submanifolds and its application to Whitney's immersion Preprint.
[4] I. Castro and F. Urbano, Lagrangian surfaces in the complex Euclidean plane with conformal Maslov form Töhoku Math. J. 45 (1993), 565-582.
[5] B. Y. Chen, Geometry of Submanifolds and its Applications, Science University of Tokyo, 1981.
[6] J. Erbacher, Reduction of the codimension of an isometric immersion J. Differential Geometry 5 (1971), 333-340.
[7] N. Ejiri, Totally real minimal immersions of n-dimensional real space forms into n-dimendional complex space forms Proc. Amer. Math. Soc. 84 (1982), 243-246.
[8] M. Gromov, Pseudo-holomorphic curves in symplectic manifolds Invent. Math. 82 (1985), 307-347.
[9] J. D. Moore, Isometric immersions of Riemannian products J. Differential Geometry 5 (1971), 159-168.
[10] J. M. Morvan, Classe de Maslov d'une immersion Lagrangienne et minimalite C. R. Acad. Sc. Paris 292 (1981), 633-636.
[11] M. Obata, Conformal transformations of Riemannian manifolds J. Differential Geometry 4 (1970), 311-333.
[12] E. A. Ruh and J. Vilms, The tension field of the Gauss map Trans. Amer. Math. Soc. 149 (1970), 569-573.
[13] Y. Suyama and Y. Tsukamoto, Riemannian manifolds admitting a certain confomal transformation group J. Differential Geometry 5 (1971), 415-426.
[14] S. Tanno and W. Weber, Closed conformal vector fields J. Differential Geometry 3 (1969), 361-366.
[15] Y. Tashiro, Complete Riemannian manifolds and some vector fields Trans. Amer. Math. Soc. 117 (1965), 251-275.
[16] F. Urbano, Totally real submanifolds Geometry and Topology of submanifolds, Worl Scientific (1989), 198-208.
[17] A. Weinstein, Lectures on symplectic manifolds Conference board of the Mathematical Sciences 29 (1977).
[18] S. T. Yau, Submanifolds with constant mean curvature I Amer. J. Math. 96 (1974), 346-366.

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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