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arXiv · 2609.23873

Orientable minimal submanifolds of low index in the sphere

Jacob Bernstein·Daniel Ketover
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Abstract

In this short note we prove a rigidity result for orientable minimal submanifolds in the round sphere of the lowest non-trivial Morse index. In particular, we show that the only closed and connected $(2m-2)$-dimensional orientable minimal submanifolds in $\mathbb{S}^{2m}$ of index less than or equal to $2m+1$ are the totally geodesic spheres.

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Jacob Bernstein, Daniel Ketover. 2026-09-20. Orientable minimal submanifolds of low index in the sphere. https://arxiv.org/abs/2609.23873

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