A CONSTRUCTION METHOD OF LAGRANGIAN SURFACES IN COMPLEX PSEUDO-EUCLIDEAN PLANE C(1,2) AND ITS APPLICATIONS

Yıl 2014, Cilt: 7 Sayı: 1, 4 - 25, 30.04.2014

Bang-yen Chen

https://doi.org/10.36890/iejg.594488

Öz

 

Anahtar Kelimeler

Lagrangian immersion, Legendre curve, Lagrangian surface of constant curvature, Hamiltonian minimal Lagrangian surfaces, Lagrangian catenoid

Kaynakça

• [1] Aiyama, R., Lagrangian surfaces in the complex 2-space, in: Proceedings of the Fifth Inter- national Workshop on Differential Geometry (Taegu, 2000), 25–29, Kyungpook Natl. Univ., Taegu, 2001.
• [2] Aiyama, R., Totally real surfaces in the complex 2-space, in: Steps in Differential Geometry (Debrecen, 2000), 15–22, Debrecen, 2001.
• [3] Castro, I. and Chen, B.-Y., Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves, Tohoku Math. J. 58 (2006) 565–579.
• [4] Castro, I. and Lerma, A. M., A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves, J. Geom. Phys. 75 (2014), 162–172.
• [5] Chen, B.-Y., Complex extensors and Lagrangian submanifolds in complex Euclidean spaces, Tohoku Math. J. 49 (1997), 277–297.
• [6] Chen, B.-Y., Interaction of Legendre curves and Lagrangian submanifolds, Israel J. Math. 99 (1997), 69–108.
• [7] Chen, B.-Y., Representation of flat Lagrangian H-umbilical submanifolds in complex Eu- clidean spaces, Tohoku Math. J. 51 (1999), 13–20.
• [8] Chen, B.-Y., Complex extensors and Lagrangian submanifolds in indefinite complex Eu- clidean spaces, Bull. Inst. Math. Acad. Sinica 31 (2003), 151–179.
• [9] Chen, B.-Y., Lagrangian surfaces of constant curvature in complex Euclidean plane, Tohoku Math J. 56 (2004), 289–298.
• [10] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex Euclidean plane, Proc. Edinburgh Math. Soc. 48 (2005), 337–364.
• [11] Chen, B.-Y., Maslovian Lagrangian surfaces of constant curvature in complex projective or complex hyperbolic planes, Math. Nachr. 278 (2005), 1242–1281.
• [12] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex complex projective planes, J. Geom. Phys. 53 (2005), 428–460.
• [13] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex hyperbolic planes, J. Geom. Phys. 55 (2005), 399–439.
• [14] Chen, B.-Y., Three additional families of Lagrangian surfaces of constant curvature in com- plex projective plane, J. Geom. Phys. 56 (2006), 666–669.
• [15] Chen, B.-Y., Construction of Lagrangian surfaces in complex Euclidean plane with Legendre curves, Kodai Math. J. 29 (2006), 84–112.
• [16] Chen, B.-Y., Classification of Lagrangian surfaces of constant curvature in complex hyperbolic planes, II, Soochow J. Math. 33 (2007), 127–165.
• [17] Chen, B.-Y., Pseudo-Riemannian Geometry, δ-invariants and Applications, World Scientific, Hackensack, NJ, 2011.
• [18] Chen, B.-Y., Classification of spherical Lagrangian submanifolds in complex Euclidean spaces, Int. Electron. J. Geom. 6 (2013), no. 2, 1–8.
• [19] Chen, B.-Y., Dillen, F., Verstraelen, L. and Vrancken, L., Lagrangian isometric immersions of a real-space-form Mn(c) into a complex-space-form M˜ n(4c), Math. Proc. Cambridge Phil. Soc. 124 (1998), 107–125.
• [20] Chen, B.-Y. and Ogiue, K., On totally real submanifolds, Trans. Amer. Math. Soc. 193(1974), 257–266.
• [21] Chen, B.-Y. and Vrancken,L., Lagrangian minimal isometric immersions of a Lorentzian real space form into a Lorentzian complex space form, Tohoku Math. J. 54 (2002), 121–143.
• [22] Joyce, D., Special Lagrangian m-folds in Cm with symmetries, Duke Math. J. 115 (2002), 1–51.
• [23] Vrancken, L., Minimal Lagrangian submanifolds with constant sectional curvature in indefi- nite complex space forms, Proc. Amer. Math. Soc. 130 (2002), 1459–1466.