Constant curved minimal CR 3-spheres in $\mathbb{C}P^n$

J. Aust. Math. Soc. 79 (2005), 1-10

Constant curved minimal CR 3-spheres in $\mathbb{C}P^n$

Zhen-Qi Li
Department of Mathematics
Nanchang University
Nanchang 330047
P. R. of China
Current address:
Lab. of Math. for Nonlinear Sciences
Fudan University
Shanghai 200433
P. R. of China
zhenqili@263.net

and

An-Min Huang
Department of Mathematics
Nanchang University
Nanchang 330047
P. R. of China
anminhuang@163.net

Abstract

In this paper we prove that minimal 3-spheres of CR type with constant sectional curvature c in the complex projective space $\mathbb{C}P^n$ are all equivariant and therefore the immersion is rigid. The curvature c of the sphere should be

for some integer $m\ge2$ , and the full dimension is

. An explicit analytic expression for such an immersion is given.

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