LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Rigidity of holomorphic curves in a hyperquadric Q4

Photo by joelfilip from unsplash

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.

Keywords: second fundamental; holomorphic curves; geometry; curves hyperquadric; rigidity holomorphic

Journal Title: Differential Geometry and its Applications
Year Published: 2019

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.