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arXiv · 1603.03877

Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric

Martha P. Dussan·Nikos Georgiou·Martin Magid
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Abstract

We investigate minimal surfaces in products of two-spheres ${\mathbb S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. Here ${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on the sphere. We compute all totally geodesic surfaces and we give a relation between minimal surfaces and the solutions of the Gordon equations. Finally, in some cases we give a topological classification of compact minimal surfaces.

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Martha P. Dussan, Nikos Georgiou, Martin Magid. 2016-03-12. Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric. https://arxiv.org/abs/1603.03877

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