## Abstract

In this paper we discuss a classification problem of homogeneous 2-spheres in the complex Grassmann manifold G(k+1,n+1) by theory of unitary representations of the 3-dimensional special unitary group SU(2). First we observe that if an immersion x:S^{2}→G(k+1,n+1) is homogeneous, then its image x(S^{2}) is a 2-dimensional ρ(SU(2))-orbit in G(k+1,n+1), where ρ:SU(2)→U(n+1) is a unitary representation of SU(2). Then we give a classification theorem of homogeneous 2-spheres in G(k+1,n+1). As an application we describe explicitly all homogeneous 2-spheres in G(2,4). Also we mention about an example of non-homogeneous holomorphic 2-sphere with constant curvature in G(2,4).

Original language | English |
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Pages (from-to) | 135-152 |

Number of pages | 18 |

Journal | Osaka Journal of Mathematics |

Volume | 50 |

Issue number | 1 |

Publication status | Published - Mar 2013 |