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Weak gravitational fields in generalized metric spaces. (English) Zbl 1052.53029

Tsagas, Grigorios (ed.), Proceedings of the conference on geometry and its applications in technology and the workshop on global analysis, differential geometry and Lie algebras, Thessaloniki, Greece, 1999. Bucharest: Geometry Balkan Press (ISBN 973-99669-9-3/pbk). BSG Proc. 6, 27-37 (2001).
On a 4-dimensional manifold \(M\), the authors study the effects of two types of deformations of the pseudo-Riemannian metric \(\gamma_{ij}\) with connection \(N\). First, a small Finslerian perturbation and then a conformal deformation are considered. For each of these deformed models, the arising \((h, v)\) metric structures on \(TM\) are given. The Einstein equations, as well as the equations of the stationary curves and their deviations in these models, are obtained.
For the entire collection see [Zbl 0990.00053].

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B50 Applications of local differential geometry to the sciences
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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