Harmonic tori in De Sitter spaces S2n1

Emma Carberry; Katharine Turner

doi:10.1007/s10711-013-9873-y

Harmonic tori in De Sitter spaces S²ⁿ₁

Emma Carberry^*, Katharine Turner

^*Corresponding author for this work

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

Abstract

We show that all superconformal harmonic immersions from genus one surfaces into de Sitter spaces S²ⁿ₁ with globally defined harmonic sequence are of finite-type and hence result merely from solving a pair of ordinary differential equations. As an application, we prove that all Willmore tori in S³ without umbilic points can be constructed in this simple way.

Original language	English
Pages (from-to)	143-155
Number of pages	13
Journal	Geometriae Dedicata
Volume	170
Issue number	1
DOIs	https://doi.org/10.1007/s10711-013-9873-y
Publication status	Published - Jun 2014
Externally published	Yes

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title = "Harmonic tori in De Sitter spaces S2n1",

abstract = "We show that all superconformal harmonic immersions from genus one surfaces into de Sitter spaces S2n1 with globally defined harmonic sequence are of finite-type and hence result merely from solving a pair of ordinary differential equations. As an application, we prove that all Willmore tori in S3 without umbilic points can be constructed in this simple way.",

keywords = "Harmonic maps and integrable systems, Harmonic maps of surfaces, Toda equations, Willmore surfaces",

author = "Emma Carberry and Katharine Turner",

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AU - Turner, Katharine

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AB - We show that all superconformal harmonic immersions from genus one surfaces into de Sitter spaces S2n1 with globally defined harmonic sequence are of finite-type and hence result merely from solving a pair of ordinary differential equations. As an application, we prove that all Willmore tori in S3 without umbilic points can be constructed in this simple way.

KW - Harmonic maps and integrable systems

KW - Harmonic maps of surfaces

KW - Toda equations

KW - Willmore surfaces

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DO - 10.1007/s10711-013-9873-y

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Harmonic tori in De Sitter spaces S²ⁿ₁

Abstract

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