In this paper we study,using moving frames,conformal minimal two-spheres S2 immersed into a complex hyperquadric Qn equipped with the induced Fubini-Study metric from a complex projective n+1-space CPn+1.Two associate...In this paper we study,using moving frames,conformal minimal two-spheres S2 immersed into a complex hyperquadric Qn equipped with the induced Fubini-Study metric from a complex projective n+1-space CPn+1.Two associated functions τX and τY are introduced to classify the problem into several cases.It is proved that τX or τY must be identically zero if f:S2 → Qn is a conformal minimal immersion.Both the Gaussian curvature K and the Khler angle θ are constant if the conformal immersion is totally geodesic.It is also shown that the conformal minimal immersion is totally geodesic holomorphic or antiholomorphic if K = 4.Excluding the case K = 4,conformal minimal immersion f:S2 → Q2 with Gaussian curvature K2 must be totally geodesic with(K,θ) ∈ {(2,0),(2,π/2),(2,π)}.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11071248)Knowledge Innovation Funds of CAS (Grant No.KJCX3-SYW-S03)the President Fund of GUCAS
文摘In this paper we study,using moving frames,conformal minimal two-spheres S2 immersed into a complex hyperquadric Qn equipped with the induced Fubini-Study metric from a complex projective n+1-space CPn+1.Two associated functions τX and τY are introduced to classify the problem into several cases.It is proved that τX or τY must be identically zero if f:S2 → Qn is a conformal minimal immersion.Both the Gaussian curvature K and the Khler angle θ are constant if the conformal immersion is totally geodesic.It is also shown that the conformal minimal immersion is totally geodesic holomorphic or antiholomorphic if K = 4.Excluding the case K = 4,conformal minimal immersion f:S2 → Q2 with Gaussian curvature K2 must be totally geodesic with(K,θ) ∈ {(2,0),(2,π/2),(2,π)}.
