A note on the existence of horizontal envelopes in the 3D-Heisenberg group
J. Korean Math. Soc. 2020 Vol. 57, No. 2, 415-427
https://doi.org/10.4134/JKMS.j190098
Published online March 1, 2020
Yen-Chang Huang
National University of Tainan
Abstract : By using the support functions on the $xy$-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.
Keywords : Sub-Riemannian manifolds, pseudo-hermitian geometry, envelo\-pes
MSC numbers : Primary 53C17; Secondary 53C65, 53C23
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