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doi:10.1007/s11464-021-0902-0

Front. Math. China

2021, Vol. 16

Issue (3) : 901-923 https://doi.org/10.1007/s11464-021-0902-0

RESEARCH ARTICLE

Minimal two-spheres with constant curvature in

ℍ P n

Shaoteng ZHANG(

), Xiaoxiang JIAO

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

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Abstract

We study conformal minimal two-spheres immersed into the quaternionic projective space $ℍ P n$ by using the twistor map. We present a method to construct new minimal two-spheres with constant curvature in $ℍ P n$ , based on the minimal property and horizontal condition of Veronese map in complex projective space. Then we construct some concrete examples of conformal minimal two-spheres in $ℍ P n$ with constant curvature 2/n, n = 4, 5, 6, respectively. Finally, we prove that there exist conformal minimal two-spheres with constant curvature 2/n in $ℍ P n$ (n≥7):

Keywords Quaternionic projective space twistor map minimal two-spheres Veronese sequence

Corresponding Author(s): Shaoteng ZHANG

Issue Date: 14 July 2021

Cite this article:

Shaoteng ZHANG,Xiaoxiang JIAO. Minimal two-spheres with constant curvature in

ℍ P n

[J]. Front. Math. China, 2021, 16(3): 901-923.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0902-0
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I3/901

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