Superminimal surfaces in hyperquadric Q 2

Jun Wang; Jie Fei

doi:10.1007/s11464-020-0862-9

Superminimal surfaces in hyperquadric Q ₂

Jun Wang
, Jie Fei^*

^*Corresponding author for this work

Nanjing Normal University

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

Abstract

We study a superminimal surface M immersed into a hyperquadric Q₂ in several cases classified by two global defined functions τ_X and τ_Y, which were introduced by X. X. Jiao and J. Wang to study a minimal immersion f:M → Q₂. In case both τ_X and τ_Y are not identically zero, it is proved that f is superminimal if and only if f is totally real or i ○ f:M → ℂP³ is also minimal, where i:Q₂ → ℂP³ is the standard inclusion map. In the rest case that τ_X ≡ 0 or τ_Y ≡ 0, the minimal immersion f is automatically superminimal. As a consequence, all the superminimal two-spheres in Q₂ are completely described.

Original language	English
Pages (from-to)	1035-1046
Number of pages	12
Journal	Frontiers of Mathematics in China
Volume	15
Issue number	5
DOIs	https://doi.org/10.1007/s11464-020-0862-9
Publication status	Published - Oct 2020

Keywords

53C42
53C55
Hyperquadric
holomorphic
superminimal surface
totally real

Access to Document

10.1007/s11464-020-0862-9

Cite this

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title = "Superminimal surfaces in hyperquadric Q 2",

abstract = "We study a superminimal surface M immersed into a hyperquadric Q2 in several cases classified by two global defined functions τX and τY, which were introduced by X. X. Jiao and J. Wang to study a minimal immersion f:M → Q2. In case both τX and τY are not identically zero, it is proved that f is superminimal if and only if f is totally real or i ○ f:M → ℂP3 is also minimal, where i:Q2 → ℂP3 is the standard inclusion map. In the rest case that τX ≡ 0 or τY ≡ 0, the minimal immersion f is automatically superminimal. As a consequence, all the superminimal two-spheres in Q2 are completely described.",

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AB - We study a superminimal surface M immersed into a hyperquadric Q2 in several cases classified by two global defined functions τX and τY, which were introduced by X. X. Jiao and J. Wang to study a minimal immersion f:M → Q2. In case both τX and τY are not identically zero, it is proved that f is superminimal if and only if f is totally real or i ○ f:M → ℂP3 is also minimal, where i:Q2 → ℂP3 is the standard inclusion map. In the rest case that τX ≡ 0 or τY ≡ 0, the minimal immersion f is automatically superminimal. As a consequence, all the superminimal two-spheres in Q2 are completely described.

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KW - holomorphic

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