This article is cited in 9 papers

Two-dimensional Helmholtz spaces

V. A. Kyrov

Gorno-Altaisk State University

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.

UDC: 514.76

Received: 17.04.2003
Revised: 29.06.2005

 English version: Siberian Mathematical Journal, 2005, 46:6, 1082–1096

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