Abstract In this paper, firstly, we obtain the Gauss equation and Codazzi equations of a holomorphic curve in a hyperquadric Q n , and we also compute the Laplace of… Click to show full abstract
Abstract In this paper, firstly, we obtain the Gauss equation and Codazzi equations of a holomorphic curve in a hyperquadric Q n , and we also compute the Laplace of the square of the length of the second fundamental form. Secondly, we prove that any two linearly full holomorphic curves in Q 4 are congruent if their first and second fundamental forms are the same. Finally, we determine a one-parameter family of homogeneous holomorphic curves in Q 4 with constant curvature 2, but their second fundamental forms are different.
               
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