Chebyshev nets formed by Ricci curves in a 3-dimensional Weyl space


Yildirim G., Ozdeger A.

TOPOLOGY AND ITS APPLICATIONS, vol.153, pp.350-358, 2005 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 153
  • Publication Date: 2005
  • Doi Number: 10.1016/j.topol.2003.05.011
  • Title of Journal : TOPOLOGY AND ITS APPLICATIONS
  • Page Numbers: pp.350-358

Abstract

In this paper, Ricci curves in a 3-dimensional Weyl space W-3(g, T) are defined and it is shown that any 3-dimensional Chebyshev net formed by the three families of Ricci curves in a W-3(g, T) having a definite metric and Ricci tensors is either a geodesic net or it consists of a geodesic subnet the members of which have vanishing second curvatures. In the case of in indefinite Ricci tensor, only one of the members of the geodesic subnet under consideration has a vanishing second curvature. (c) 2004 Elsevier B.V. All rights reserved.