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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 6, Pages 1341–1359 (Mi smj1044)  
This article is cited in 7 scientific papers (total in 7 papers)

Two-dimensional Helmholtz spaces

V. A. Kyrov

Gorno-Altaisk State University
Full-text PDF (261 kB) Citations (7)
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Abstract: We study two-dimensional manifolds whose infinitesimally small neighborhoods have the structures of Helmholtz planes. We deal with the main objects related to Helmholtz spaces: in particular, we determine the metric function $f$ and introduce the concept of quasimetric connection and geodesic. For some Helmholtz spaces we prove the existence of isothermal coordinates.
Keywords: Helmholtz plane, Helmholtz manifold, metric function, structure functions, quasimetric connection, isothermal coordinates, quasilength.
Received: 17.04.2003
Revised: 29.06.2005
English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 6, Pages 1082–1096
DOI: https://doi.org/10.1007/s11202-005-0103-1
Bibliographic databases:
UDC: 514.76
Language: Russian
Citation: V. A. Kyrov, “Two-dimensional Helmholtz spaces”, Sibirsk. Mat. Zh., 46:6 (2005), 1341–1359; Siberian Math. J., 46:6 (2005), 1082–1096
Citation in format AMSBIB
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\pages 1341--1359
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\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 6
\pages 1082--1096
\crossref{https://doi.org/10.1007/s11202-005-0103-1}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000234073700011}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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