Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T06:28:16.514Z Has data issue: false hasContentIssue false
  • English
  • Français

BIHARMONIC LAGRANGIAN SUBMANIFOLDS IN KÄHLER MANIFOLDS

Published online by Cambridge University Press:  25 February 2013

SHUN MAETA  and
HAJIME URAKAWA
SHUN MAETA
Affiliation:
Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan e-mail: maeta@ims.is.tohoku.ac.jp
HAJIME URAKAWA
Affiliation:
Institute for International Education, Tohoku University, Sendai 980-8576, Japan e-mail: urakawa@math.is.tohoku.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give the necessary and sufficient conditions for Lagrangian submanifolds in Kähler manifolds to be biharmonic. We classify biharmonic PNMC Lagrangian H-umbilical submanifolds in the complex space forms. Furthermore, we classify biharmonic PNMC Lagrangian surfaces in the two-dimensional complex space forms.

Keywords

Primary 58E20Secondary 53C43
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 465 - 480
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013

References

REFERENCES

1.Balmus, A., Montaldo, S. and Oniciuc, C., Biharmonic PNMC submanifolds in spheres, to appear in Ark. Mat.Google Scholar
2.Castro, I. and Urbano, F., Twistor holomorphic Lagrangian surfaces in complex projective and hyperbolic planes, Ann. Global. Anal. Geom. 13 (1995), 59–67.Google Scholar
3.Chen, B. Y., Surfaces with parallel normalized mean curvature vector, Mon. Math. 90 (1980), 185–194.CrossRefGoogle Scholar
4.Chen, B. Y., Complex extensors and Lagrangian submanifolds in complex Euclidean spaces, Tohoku Math. J. 49 (1997), 277–297.CrossRefGoogle Scholar
5.Chen, B. Y., Interaction of Legendre curves and Lagrangian submanifolds, Israel J. Math. 99 (1997), 69–108.Google Scholar
6.Chen, B. Y., Representation of flat Lagrangian H-umbilical submanifolds in complex Euclidean spaces, Tohoku Math. J. 51 (1999), 13–21.CrossRefGoogle Scholar
7.Chen, B. Y. and Ogiue, K., On totally real submanifolds, Trans. Amer. Math. Soc. 193 (1974), 257–266.CrossRefGoogle Scholar
8.Eells, J. and Lemaire, L., Selected topics in harmonic maps, CBMS Reg. Conf. Ser., vol. 50 (AMS, Providence, RI, 1983).Google Scholar
9.Fetcu, D., Loubeau, E., Montaldo, S. and Oniciuc, C., Biharmonic submanifolds of ℂPn, Math. Z. 266 (3) (2010), 505–531.Google Scholar
10.Jiang, G. Y., 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. A 7 (1986), 388–402 [English translation, Note Mat. 28 (2009), 209–232].Google Scholar
11.Sasahara, T., Biharmonic Lagrangian surfaces of constant mean curvature in complex space forms, Glasgow Math. J. 49 (2007), 497–507.Google Scholar
12.Sasahara, T., Biminimal Lagrangian H-umbilical submanifolds in complex space forms, Geom. Dedicata 160 (2012), 185–193.Google Scholar
13.Sasahara, T., A classification result for biminimal Lagrangian surfaces in complex space forms, J. Geom. Phys. 60 (2010), 884–895.Google Scholar