Maslovian Lagrangian surfaces of constant curvature in complex projective or complex hyperbolic planes

Mathematische Nachrichten

Volumn 278, Issue 11, 2005, Pages 1242-1281

  Chen, Bang Yen ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Lagrangian immersion; Legendre curve; Legendre immersion; Maslovian Lagrangian immersion; Special Legendre curve

Indexed keywords

EID: 24944483270     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.200310305     Document Type: Article

References (16)

1. B. Y. Chen, Geometry of Submanifolds (M. Dekker, New York, 1973).
2. B. Y. Chen, Complex extensors and Lagrangian submanifolds in complex Euclidean spaces, Tohoku Math. J. (2) 49, 277-297 (1997).
3. B. Y. Chen, Interaction of Legendre curves and Lagrangian submanifolds, Israel J. Math. 9, 69-108 (1997).
4. B. Y. Chen, Representation of flat Lagrangian H-umbilical submanifolds in complex Euclidean spaces, Tohoku Math. J. (2) 51, 13-20 (1999).
5. B. Y. Chen, Riemannian geometry of Lagrangian submanifolds, Taiwanese J. Math. 5, 681-723 (2001).
6. B. Y. Chen, Lagrangian surfaces of constant curvature in complex Euclidean plane, Tohoku Math. J. (2) 56, 289-298 (2004).
7. B. Y. Chen, Classification of Lagrangian surfaces of constant curvature in complex Euclidean plane, Proc. Edinb. Math. Soc. (2) 48, 337-364 (2005).
8. n(4c), Math. Proc. Cambridge Philo. Soc. 124, 107-125 (1998).
9. B. Y. Chen and O. J. Garay, Maslovian Lagrangian immersions of real space forms into complex space forms, Japan. J. Math. 30, 227-281 (2004).
10. B. Y. Chen and K. Ogiue, On totally real submanifolds, Trans. Amer. Math. Soc. 193, 257-266 (1974).
11. B. Y. Chen and K. Ogiue, Two theorems on Kaehler manifolds, Michigan Math. J. 21, 225-229 (1974).
12. N. Ejiri, Totally real minimal immersions of n-dimensional totally real space forms into n-dimensional complex space forms, Proc. Amer. Math. Soc. 84, 243-246 (1982).
13. C. Montealegre and L. Vrancken, Three dimensional Lagrangian submanifolds of the complex projective space, J. Math. Soc. Japan 53, 603-631 (2001).
14. J.-M. Morvan, Classe de Maslov d'une sous-variété Lagrangienne et minimalité, C. R. Acad. Sci. Paris Sér. I Math. 292, 633-636 (1981).
15. R. Ponge and H. Reckziegel, Twisted products in pseudo-Riemannian geometry, Geom. Dedicata 48, 15-25 (1993).
16. H. Reckziegel, Horizontal Lifts of Isometric Immersions into the Bundle Space of a Pseudo-Riemannian Submersion, Lecture Notes in Mathematics Vol. 1156 (Springer, New York 1985), pp. 264-279.