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Constant curved minimal CR 3-spheres in CPn

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Zhen-Qi Li  and
An-Min Huang
Zhen-Qi Li*
Affiliation:
Department of MathematicsNanchang UniversityNanchang 330047 P. R. ofChina
An-Min Huang
Affiliation:
Department of MathematicsNanchang Univeristy, Nanchang 330047 P. R.China e-mail: anminhuang@163.com
*
Lab. of Math. for Nonlinear Sciences Fudan University Shanghai 200433 P. R. of China e-mail: zhenqili@263.net
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Abstract

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In this paper we prove that minimal 3-spheres of CR type with constant sectional curvature c in the complex projective space CPn are all equivariant and therefore the immersion is rigid. The curvature c of the sphere should be c = 1/(m2-1) for some integer m≥ 2, and the full dimension is n = 2m2-3. An explicit analytic expression for such an immersion is given.

Keywords

minimalconstant curvatureCR-submanifoldcomplex projective space.

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53C55: Hermitian and Kählerian manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 1 - 10
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Bejancu, A., Geometry of CR-submanifolds (D. Reidel Publishing Company, Dordrecht, 1986).CrossRefGoogle Scholar
[2]Bolton, J., Jensen, G. R., Rigoli, M. and Woodward, L. M., ‘On conformal minimal immersions of S2 into CPn’, Math. Ann. 279 (1988), 599–620.Google Scholar
[3]Chen, B. Y., Dillen, F., Verstraelen, L. and Vrancken, L., ‘An exotic totally real minimal immersion of S3 in CP3 and its characterization’, Proc. Roy. Soc. Edinburgh Sect.A 126 (1996), 153–165.Google Scholar
[4]Chen, B. Y., Dillen, F., Verstraelen, L. and Vrancken, L., ‘Lagrangian isometric immersions of a real space form Mn (c) into complex space form Mn(4c)’, Math. Proc. Cambridge Philos. Soc. 124 (1998), 107–125.Google Scholar
[5]Li, Z. Q., ‘Minimal S3 with constant curvature in CPn’, J. London Math. Soc. (2) 68 (2003), 223–240.Google Scholar
[6]Ogiue, K., ‘Differential geometry of Kaehler submanifolds’, Adv. Math. 13 (1974), 73–114.Google Scholar