Abstract
In this paper, Ricci curves in a 3-dimensional Weyl space W3 (g, T) are defined and it is shown that any 3-dimensional Chebyshev net formed by the three families of Ricci curves in a W3(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 an indefinite Ricci tensor, only one of the members of the geodesic subnet under consideration has a vanishing second curvature.
Original language | English |
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Pages (from-to) | 350-358 |
Number of pages | 9 |
Journal | Topology and its Applications |
Volume | 153 |
Issue number | 2-3 SPEC. ISS. |
DOIs | |
Publication status | Published - 1 Sept 2005 |
Keywords
- Chebyshev net
- Geodesic net
- Ricci curve
- Weyl space