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arXiv · 2406.09927

Index estimates for harmonic Gauss maps

Alcides de Carvalho·Marcos P. Cavalcante·Wagner Costa-Filho·Darlan de Oliveira
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Abstract

Let $\Sigma$ denote a closed surface with constant mean curvature in $\mathbb{G}^3$, a 3-dimensional Lie group equipped with a bi-invariant metric. For such surfaces, there is a harmonic Gauss map which maps values to the unit sphere within the Lie algebra of $\mathbb{G}$. We prove that the energy index of the Gauss map of $\Sigma$ is bounded below by its topological genus. We also obtain index estimates in the case of complete non compact surfaces.

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Alcides de Carvalho, Marcos P. Cavalcante, Wagner Costa-Filho, Darlan de Oliveira. 2024-06-14. Index estimates for harmonic Gauss maps. https://arxiv.org/abs/2406.09927

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