{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:31:11Z","timestamp":1775464271652,"version":"3.50.1"},"reference-count":6,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T00:00:00Z","timestamp":1611273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.11771070"],"award-info":[{"award-number":["No.11771070"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of this paper was to obtain Gauss\u2013Bonnet theorems on the Lorentzian Heisenberg group and the Lorentzian group of rigid motions of the Minkowski plane. At the same time, the sub-Lorentzian limits of Gaussian curvature for surfaces which are C2-smooth in the Lorentzian Heisenberg group away from characteristic points and signed geodesic curvature for curves which are C2-smooth on surfaces are studied. Using a similar method, we also studied the corresponding contents on Lorentzian group of rigid motions of the Minkowski plane.<\/jats:p>","DOI":"10.3390\/sym13020173","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T12:28:31Z","timestamp":1611577711000},"page":"173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Gauss\u2014Bonnet Theorems in the Lorentzian Heisenberg Group and the Lorentzian Group of Rigid Motions of the Minkowski Plane"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4591-2463","authenticated-orcid":false,"given":"Sining","family":"Wei","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1007\/s10883-016-9338-3","article-title":"Gauss-Bonnet theorem in sub-Riemannian Heisenberg space","volume":"22","author":"Diniz","year":"2016","journal-title":"J. Dyn. Control Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00209-016-1815-6","article-title":"Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group","volume":"287","author":"Balogh","year":"2017","journal-title":"Math. Z."},{"key":"ref_3","unstructured":"Veloso, M. (2019). Rotation Surfaces of Constant Gaussian Curvature as Riemannian Approximation Scheme in Sub-Riemannian Heisenberg Space \u210d1. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.geomphys.2014.11.006","article-title":"Analytic continuation, the Chern-Gauss-Bonnet theorem, and the Euler-Lagrange equations in Lovelock theory for indefinite signature metrics","volume":"88","author":"Gilkey","year":"2015","journal-title":"J. Geom. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, Y., and Wei, S. (2020). Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane. Sci. China Math., 1\u201318.","DOI":"10.1007\/s11425-019-1667-5"},{"key":"ref_6","unstructured":"Capogna, L., Danielli, D., Pauls, S., and Tyson, J. (2007). An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem, Springer Science & Business Media."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/173\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:14:00Z","timestamp":1760159640000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,22]]},"references-count":6,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020173"],"URL":"https:\/\/doi.org\/10.3390\/sym13020173","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,22]]}}}