In the sub-Riemannian Heisenberg group Hn, with 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 H2, marking a significant step towards understanding the sub-Riemannian Bernstein problem.
A Characterization of Horizontally Totally Geodesic Hypersurfaces in Heisenberg Groups / Pinamonti, A.; Verzellesi, S.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 35:8(2025). [10.1007/s12220-025-02071-8]
A Characterization of Horizontally Totally Geodesic Hypersurfaces in Heisenberg Groups
Pinamonti A.;Verzellesi S.
2025-01-01
Abstract
In the sub-Riemannian Heisenberg group Hn, with 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 H2, marking a significant step towards understanding the sub-Riemannian Bernstein problem.File in questo prodotto:
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