Rigidity of holomorphic curves in a hyperquadric Q                         4

Jie Fei; Jun Wang

doi:10.1016/j.difgeo.2019.03.006

Rigidity of holomorphic curves in a hyperquadric Q ₄

Jie Fei
, Jun Wang^*

^*Corresponding author for this work

Nanjing Normal University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	78-92
Number of pages	15
Journal	Differential Geometry and its Application
Volume	65
DOIs	https://doi.org/10.1016/j.difgeo.2019.03.006
Publication status	Published - Aug 2019

Keywords

Holomorphic immersion
Hyperquadric
Rigidity
The first fundamental form
The second fundamental form

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10.1016/j.difgeo.2019.03.006

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title = " Rigidity of holomorphic curves in a hyperquadric Q 4 ",

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 = "Holomorphic immersion, Hyperquadric, Rigidity, The first fundamental form, The second fundamental form",

author = "Jie Fei and Jun Wang",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = aug,

doi = "10.1016/j.difgeo.2019.03.006",

language = "English",

volume = "65",

pages = "78--92",

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T1 - Rigidity of holomorphic curves in a hyperquadric Q 4

AU - Fei, Jie

AU - Wang, Jun

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 - https://www.scopus.com/pages/publications/85063670517

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 -

Rigidity of holomorphic curves in a hyperquadric Q ₄

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Keywords

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