Equivariant totally real 3-spheres in the complex projective space C{double-struck}P{double-struck} ~n

摘要

In this paper we study the equivariant totally real immersions from S ~3 into C{double-struck}P{double-struck} ~n. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} ~n, and characterize the minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} ~n by the standard example. We also give many minimal linearly full isometric immersions from S1/53 into C{double-struck}P{double-struck} ~7, C{double-struck}P{double-struck} ~(11) and C{double-struck}P{double-struck} ~(15). As an application of our method, we classify equivariant Lagrangian S ~3 in C{double-struck}P{double-struck} ~3 again.