TY - JOUR
T1 - Rigidity of holomorphic curves in a hyperquadric Q 4
AU - Fei, Jie
AU - Wang, Jun
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/8
Y1 - 2019/8
N2 - 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.
AB - 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.
KW - Holomorphic immersion
KW - Hyperquadric
KW - Rigidity
KW - The first fundamental form
KW - The second fundamental form
UR - http://www.scopus.com/inward/record.url?scp=85063670517&partnerID=8YFLogxK
U2 - 10.1016/j.difgeo.2019.03.006
DO - 10.1016/j.difgeo.2019.03.006
M3 - Article
AN - SCOPUS:85063670517
SN - 0926-2245
VL - 65
SP - 78
EP - 92
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
ER -