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arXiv · 2509.22253

The twistor lifts of surfaces in 4-spaces

Naoya Ando
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Abstract

This is a survey of the twistor lifts of surfaces in $4$-dimensional spaces. In most part of this survey, the space is Euclidean $4$-space $E^4$. The definitions of the Gauss maps and the twistor lifts of surfaces in $E^4$ are given by orthogonal complex structures of $E^4$. Based on these definitions, we can understand holomorphicity of the Gauss maps of minimal surfaces in $E^4$ and isotropicity of such surfaces.

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Naoya Ando. 2025-09-26. The twistor lifts of surfaces in 4-spaces. https://arxiv.org/abs/2509.22253

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