Algebraic minimal surfaces in $\mathsf R^4$

Authors

  • Anthony Small

DOI:

https://doi.org/10.7146/math.scand.a-14432

Abstract

There exists a natural correspondence between null curves in $\mathbf{C}^4$ and "free" curves on $\mathcal O(1)\oplus \mathcal O(1)$; it underlies the existence of "Weierstrass type formulae" for minimal surfaces in $\mathbf{R}^4$. The construction determines correspondences for minimal surfaces in $\mathbf{R}^3$, and constant mean curvature 1 surfaces in $\mathrm{H}^3$; moreover it facilitates the study of symmetric minimal surfaces in $\mathbf{R}^4$.

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Published

2004-03-01

How to Cite

Small, A. (2004). Algebraic minimal surfaces in $\mathsf R^4$. MATHEMATICA SCANDINAVICA, 94(1), 109–124. https://doi.org/10.7146/math.scand.a-14432

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Articles