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^*

^*Corresponding author for this work

University of Chinese Academy of Sciences

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

3 Citations (Scopus)

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’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.

Original language	English
Pages (from-to)	2063-2076
Number of pages	14
Journal	Annali di Matematica Pura ed Applicata
Volume	196
Issue number	6
DOIs	https://doi.org/10.1007/s10231-017-0653-4
Publication status	Published - 1 Dec 2017
Externally published	Yes

Keywords

Conformal minimal surface
Quaternionic projective space
Twistor map

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10.1007/s10231-017-0653-4

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title = "Conformal minimal surfaces immersed into HPn ",

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.",

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AU - Jiao, Xiaoxiang

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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

IS - 6

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Conformal minimal surfaces immersed into HPⁿ

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Keywords

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