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THE MINIMAL $S^{3}$ WITH CONSTANT SECTIONAL CURVATURE IN $\mathit{CP}^{n}$

Published online by Cambridge University Press:  18 February 2015

SEN HU
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, China Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei 230026, Anhui, China email shu@ustc.edu.cn
KANG LI*
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, China email likang@mail.ustc.edu.cn
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Abstract

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It is known that the minimal 3-spheres of CR type with constant sectional curvature have been classified explicitly, and also that the weakly Lagrangian case has been studied. In this paper, we provide some examples of minimal 3-spheres with constant curvature in the complex projective space, which are neither of CR type nor weakly Lagrangian, and give the adapted frame of a minimal 3-sphere of CR type with constant sectional curvature.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Bando, S. and Ohnita, Y., ‘Minimal 2-spheres with constant curvature in CP n’, J. Math. Soc. Japan 3 (1987), 477487.Google Scholar
Bolton, J., Jensen, G. R., Rigoli, M. and Woodward, L. M., ‘On conformal minimal immersions of S 2 into CP n’, Math. Ann. 279 (1988), 599620.CrossRefGoogle Scholar
Chen, Q., Hu, S. and Xu, X., ‘Construction of Lagrangian submanifolds in CP n’, Pacific J. Math. 285(1) (2012), 3149.CrossRefGoogle Scholar
Chern, S. S. and Wolfson, J., ‘Minimal surfaces by moving frames’, Amer. J. Math. 105 (1983), 5983.CrossRefGoogle Scholar
Fei, J., Peng, C. and Xu, X., ‘Equivariant totally real 3-spheres in the complex projective space CP n’, Differential Geom. Appl. 30 (2012), 262273.CrossRefGoogle Scholar
Li, Z. Q., ‘Minimal S 3 with constant curvature in CP n’, J. Lond. Math. Soc. (2) 68 (2003), 223240.CrossRefGoogle Scholar
Li, Z. Q. and Huang, A. M., ‘Constant curved minimal CR 3-spheres in CP n’, J. Aust. Math. Soc. 79 (2005), 110.CrossRefGoogle Scholar
Li, Z. Q. and Tao, Y. Q., ‘Equivariant Lagrangian minimal S 3 in CP n’, Acta Math. Sin. (Engl. Ser.) 22 (2006), 12151220.CrossRefGoogle Scholar