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arXiv · 2007.01963

Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3

Berenice Zavala
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Abstract

We find a spinorial representation of a Riemannian or Lorentzian surface in a Lorentzian homogeneous space of dimension $3.$ We in particular obtain a representation theorem for surfaces in the $\mathbb{L}(\kappa,\tau)$ spaces. We then recover the Calabi correspondence between minimal surfaces in $\mathbb{R}^3$ and maximal surfaces in $\mathbb{R}_1^3$, and obtain a new Lawson type correspondence between CMC surfaces in $\mathbb{R}_1^3$ and in the 3-dimensional pseudo-hyperbolic space $\mathbb{H}_1^{3}.$

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Berenice Zavala. 2020-07-03. Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3. https://doi.org/10.1007/s00006-022-01205-3

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