Conformal minimal surfaces immersed into HPn

Xiaodong Chen; Xiaoxiang Jiao

doi:10.1007/s10231-017-0653-4

Conformal minimal surfaces immersed into HPⁿ

Xiaodong Chen, Xiaoxiang Jiao^*

^*此作品的通讯作者

University of Chinese Academy of Sciences

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

In this paper, we want to construct conformal minimal surfaces and conformal minimal two-spheres in HPⁿ by the twistor map π: CP² ⁿ ⁺ ¹→ HPⁿ. The construction is due to Eells and Wood’s conclusion about the composition of a horizontal harmonic map in 1983. Firstly, we give a characterization of horizontal holomorphic surfaces in CP⁵. Under this characterization, we construct eight families of conformal minimal surfaces in HP². Then, we study horizontal Veronese sequences in CP⁴ and CP⁵, and we transform the construction into solving a quadratic equation. Based on this, we get some examples of conformal minimal two-spheres in HP² with constant curvature 45 and 413.

源语言	英语
页（从-至）	2063-2076
页数	14
期刊	Annali di Matematica Pura ed Applicata
卷	196
期	6
DOI	https://doi.org/10.1007/s10231-017-0653-4
出版状态	已出版 - 1 12月 2017
已对外发布	是

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Chen, X., & Jiao, X. (2017). Conformal minimal surfaces immersed into HPⁿ Annali di Matematica Pura ed Applicata, 196(6), 2063-2076. https://doi.org/10.1007/s10231-017-0653-4

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abstract = "In this paper, we want to construct conformal minimal surfaces and conformal minimal two-spheres in HPn by the twistor map π: CP2 n + 1→ HPn. The construction is due to Eells and Wood{\textquoteright}s conclusion about the composition of a horizontal harmonic map in 1983. Firstly, we give a characterization of horizontal holomorphic surfaces in CP5. Under this characterization, we construct eight families of conformal minimal surfaces in HP2. Then, we study horizontal Veronese sequences in CP4 and CP5, and we transform the construction into solving a quadratic equation. Based on this, we get some examples of conformal minimal two-spheres in HP2 with constant curvature 45 and 413.",

keywords = "Conformal minimal surface, Quaternionic projective space, Twistor map",

author = "Xiaodong Chen and Xiaoxiang Jiao",

note = "Publisher Copyright: {\textcopyright} 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.",

year = "2017",

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doi = "10.1007/s10231-017-0653-4",

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AB - In this paper, we want to construct conformal minimal surfaces and conformal minimal two-spheres in HPn by the twistor map π: CP2 n + 1→ HPn. The construction is due to Eells and Wood’s conclusion about the composition of a horizontal harmonic map in 1983. Firstly, we give a characterization of horizontal holomorphic surfaces in CP5. Under this characterization, we construct eight families of conformal minimal surfaces in HP2. Then, we study horizontal Veronese sequences in CP4 and CP5, and we transform the construction into solving a quadratic equation. Based on this, we get some examples of conformal minimal two-spheres in HP2 with constant curvature 45 and 413.

KW - Conformal minimal surface

KW - Quaternionic projective space

KW - Twistor map

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JF - Annali di Matematica Pura ed Applicata

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Conformal minimal surfaces immersed into HPn

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Conformal minimal surfaces immersed into HPⁿ