Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008
qr-code QR
Code

Article

HOME ALL ARTICLES View

J. Korean Math. Soc. 2020; 57(2): 415-427

Online first article February 13, 2020      Printed March 1, 2020

https://doi.org/10.4134/JKMS.j190098

Copyright © The Korean Mathematical Society.

A note on the existence of horizontal envelopes in the 3D-Heisenberg group

Yen-Chang Huang

National University of Tainan

Abstract

Go to

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

Supported by: This work was supported by the Ministry of Science and Technology of Taiwan(Grant No.108-2115-M-227-001-MY2).

Article Tools

Stats or Metrics

Share this article on :

Related articles in JKMS