• Minimal surfaces in symmetric spaces with parallel second fundamental form

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    • Keywords


      Isometric minimal immersion; Gaussian curvature; Kähler angle; second fundamental form; symmetric space

    • Abstract


      In this paper, we study geometry of isometric minimal immersions of Riemannian surfaces in a symmetric space by moving frames and prove that the Gaussian curvature must be constant if the immersion is of parallel second fundamental form. In particular, when the surface is $S^2$, we discuss the special case and obtain a necessary and sufficient condition such that its second fundamental form is parallel. We alsoconsider isometric minimal two-spheres immersed in complex two-dimensional Kählersymmetric spaces with parallel second fundamental form, and prove that the immersionis totally geodesic with constant Kähler angle if it is neither holomorphic nor antiholomorphicwith Kähler angle $\alpha\neq 0$ (resp. $\alpha\neq \pi$) everywhere on $S^2$.

    • Author Affiliations



      1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China
      2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
    • Dates

  • Proceedings – Mathematical Sciences | News

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