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We investigate quasi-minimal Lagrangian surfaces whose mean curvature vectors are eigenvectors of the Laplace operator.
Wydawca
Czasopismo
Rocznik
Tom
Strony
185--196
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
Bibliografia
- [1] M. Barros and O. J. Garay, On submanifolds with harmonic mean curvature, Proc. Amer. Math. Soc. 123 (1995), 2545-2549.
- [2] M. Barros and A. Romero, Indefinite Kaehler manifolds, Math. Ann. 261 (1982), 55-62.
- [3] R. Caddeo, S. Montaldo and C. Oniciuc, Biharmonic submanifolds of S3, Internat. J. Math. 12 (2001), 867-876.
- [4] B.-Y. Chen, Null 2-type surfaces in E3 are circular cylinders, Kodai Math. J. 11 (1988), 295-299 .
- [5] B.-Y. Chen, Null2-type surfaces in Euclidean space, Algebra, Analysis and Geometry (1988), 1-18.
- [6] B.-Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), 117-337.
- [7] B.-Y. Chen, Riemannian geometry of Lagrangian submanifolds, Taiwanese J. Math. 5 (2001) 681-723.
- [8] B.-Y. Chen and S. Ishikawa, Biharmonic pseudo-Riemannian submanifolds in Euclidean spaces, Kyushu J. Math. 52 (1998), 167-185.
- [9] B.-Y. Chen and L. Vrancken, Lagrangian minimal isometric immersion of a Lorentzian real space form into a Lorentzian complex space form, Tohoku M. J. 54 (2002), 121-143.
- [10] I. Dimitric, Submanifolds of Em with harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica. 20 (1992), 53-65.
- [11] J. Eells and J. H. Sampson, Variational theory in fiber bundles, Proc. U.S.-Japan Seminar in Differential Geometry (Kyoto 1965), pp. 22-33.
- [12] A. Ferrández, P. Lucas and M. A. Meroño, Biharmonic Hopf cylinders, Rocky Mountain J. Math. 28 (1998), 957-975.
- [13] T. Hasanis and T . Vlachos, Hypersurfaces in E4 with harmonic mean curvature vector field, Math. Nachr. 172 (1995), 145-169.
- [14] J . Inoguchi, Submanifolds with harmonic mean curvature vector field in contact 3-manifolds, Colloq. Math. 100 (2004), 163-179.
- [15] G. Y. Jiang, 2-harmonic isometric immersions between Riemannian manifolds, (Chinese), Chinese Ann. Math. A 7 (1986), 130-144.
- [16] G. Y. Jiang, 2-harmonic maps and their first and second variational formulas. (Chinese), Chinese Ann. Math. A 7 (1986), 389-402.
- [17] M. Kriele and L. Vrancken, Minimal Lagrangian submanifolds of Lorentzian complex space forms with constant sectional curvature, Arch. Math. 72 (1999), 223-232.
- [18] T. Sasahara, Spectral decomposition of the mean curvature vector field of surfaces in a Sasakian manifold R2n+1(-3), Results. Math. 43 (2003), 168-180.
- [19] T. Sasahara, Legendre surfaces whose mean curvature vectors are eigenvectors of the Laplace operator, Note. Mat. 22 (2003), 48-58.
- [20] A. Strominger, S.-T. Yau and E. Zaslow, Mirror symmetry is T-duality, Nuclear Phys. B 479 (1996), 243-259.
- [21] L. Vrancken, Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms, Proc. Amer. Math. Soc. 130 (2002), 1459-1466.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0012-0020