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arXiv · 2301.12214

Index bounds for closed minimal surfaces in 3-manifolds with the Killing property

Marcos P. Cavalcante·Darlan F. de Oliveira·Robson dos S. Silva
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Abstract

Let $\Sigma$ be a closed minimal surface immersed in a Riemannian 3-manifold carrying an orthonormal Killing frame. This class of ambient spaces includes Lie groups with a bi-invariant metric. In this paper, we prove that the sum of the Morse index and the nullity of $\Sigma$ is bounded from below by a constant times its genus.

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Marcos P. Cavalcante, Darlan F. de Oliveira, Robson dos S. Silva. 2023-01-28. Index bounds for closed minimal surfaces in 3-manifolds with the Killing property. https://doi.org/10.21711/231766362022%2Frmc4914

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