A Characterization of Horizontally Totally Geodesic Hypersurfaces in Heisenberg Groups

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2025年6月24日

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Andrea Pinamonti,
Simone Verzellesi

摘要

In the sub-Riemannian Heisenberg group $\mathbb {H}^n$ $H^{n}$ , with $n \geqslant 2$ $n ⩾ 2$ , we prove that hyperplanes are the only entire hypersurfaces with vanishing horizontal symmetric second fundamental form. This result is applied in a subsequent work to establish a Bernstein-type theorem in $\mathbb {H}^2$ $H^{2}$ , marking a significant step towards understanding the sub-Riemannian Bernstein problem.