Local rigidity of minimal surfaces in a hyperquadric Q2

Jie Fei; Jun Wang

doi:10.1016/j.geomphys.2018.05.017

Local rigidity of minimal surfaces in a hyperquadric Q₂

Jie Fei
, Jun Wang^*

^*Corresponding author for this work

Department of Pure Mathematics

Nanjing Normal University

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

10 Citations (Scopus)

Abstract

In this paper, we study rigidity of a minimal immersion f from a surface M into a hyperquadric Q₂. It is proved that except a case that f is totally geodesic, totally real with Gauss curvature K=0, then up to a rigidity, f is uniquely determined by the first fundamental form, the second fundamental form and Kähler angle.

Original language	English
Pages (from-to)	17-25
Number of pages	9
Journal	Journal of Geometry and Physics
Volume	133
DOIs	https://doi.org/10.1016/j.geomphys.2018.05.017
Publication status	Published - Nov 2018

Keywords

Hyperquadric
Kähler angle
Minimal immersion
Rigidity
The first fundamental form
The second fundamental form

Access to Document

10.1016/j.geomphys.2018.05.017

Cite this

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title = "Local rigidity of minimal surfaces in a hyperquadric Q2 ",

abstract = "In this paper, we study rigidity of a minimal immersion f from a surface M into a hyperquadric Q2. It is proved that except a case that f is totally geodesic, totally real with Gauss curvature K=0, then up to a rigidity, f is uniquely determined by the first fundamental form, the second fundamental form and K{\"a}hler angle.",

keywords = "Hyperquadric, K{\"a}hler angle, Minimal immersion, Rigidity, The first fundamental form, The second fundamental form",

author = "Jie Fei and Jun Wang",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

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doi = "10.1016/j.geomphys.2018.05.017",

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AU - Fei, Jie

AU - Wang, Jun

PY - 2018/11

Y1 - 2018/11

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AB - In this paper, we study rigidity of a minimal immersion f from a surface M into a hyperquadric Q2. It is proved that except a case that f is totally geodesic, totally real with Gauss curvature K=0, then up to a rigidity, f is uniquely determined by the first fundamental form, the second fundamental form and Kähler angle.

KW - Hyperquadric

KW - Kähler angle

KW - Minimal immersion

KW - Rigidity

KW - The first fundamental form

KW - The second fundamental form

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U2 - 10.1016/j.geomphys.2018.05.017

DO - 10.1016/j.geomphys.2018.05.017

M3 - Article

AN - SCOPUS:85050634071

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VL - 133

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JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics