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Stability of Biharmonic Legendrian Submanifolds in Sasakian Space Forms

Published online by Cambridge University Press:  20 November 2018

Toru Sasahara
Toru Sasahara*
Affiliation:
Department of System and Information Technology, Hachinohe Institute of Technology, 88-1 Ohbiraki Myo Hachinohe Aomori, 031-8501, Japan. e-mail: sasahara@hi-tech.ac.jp
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Abstract

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Biharmonic maps are defined as critical points of the bienergy. Every harmonic map is a stable biharmonic map. In this article, the stability of nonharmonic biharmonic Legendrian submanifolds in Sasakian space forms is discussed.

Keywords

53C4253C40biharmonic mapsSasakian manifoldsLegendrian submanifolds

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 3 , 01 September 2008 , pp. 448 - 459
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Baird, P. and Kamissoko, D., On constructing biharmonic maps and metrics. Ann. Global Anal. Geom. 23(2003), no. 1, 65–75.Google Scholar
[2] Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics 203, Birkhäuser Boston, Boston, MA, 2002.Google Scholar
[3] Caddeo, R., Montaldo, S., and Oniciuc, C., Biharmonic submanifolds of S 3 . Internat. J. Math. 12(2001), no. 8, 867–876.Google Scholar
[4] Caddeo, R., Montaldo, S., and Oniciuc, C., Biharmonic submanifolds in spheres. Israel J. Math. 130(2002), 109–123.Google Scholar
[5] Chen, B.-Y., Total Mean Curvature and Submanifold of Finite Type. Series in Pure Mathematics 1, World Scientific Publishing, Singapore, 1984.Google Scholar
[6] Chen, B.-Y., A report on submanifolds of finite type. Soochow J. Math. 22(1996), no. 2, 117–337.Google Scholar
[7] Decruyenaere, F., Dillen, F., Verstraelen, L., and Vrancken, L., The semiring of immersions of manifolds. Beiträge Algebra Geom. 34(1993), no. 2, 209–215.Google Scholar
[8] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86(1964), 109–160.Google Scholar
[9] Inoguchi, J., Submanifolds with harmonic mean curvature vector field in contact 3-manifolds. Colloq. Math. 100(2004), no. 2, 163–179.Google Scholar
[10] Jiang, G. Y., 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A 7(1986), 389–402 (Chinese).Google Scholar
[11] Oniciuc, C., On the second variation formula for biharmonic maps to a sphere. Publ. Math. Debrecen. 61(2002), no. 3–4, 613–622.Google Scholar
[12] Sasahara, T., Legendre surfaces in Sasakian space forms whose mean curvature vectors are eigenvectors. Publ. Math. Debrecen. 67(2005), no. 3–4, 285–303.Google Scholar
[13] Yano, K. and Kon, M., Structures on manifolds. Series in Pure Mathematics, 3, World Scientific Publishing, Singapore, 1984.Google Scholar