Quadratic Lagrangians and Palatini's device
- 1 August 1979
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 12 (8) , 1229-1234
- https://doi.org/10.1088/0305-4470/12/8/017
Abstract
The author deals with the mutual inequivalence of g-variation and P-variation of a given action S, the components of linear connection Gamma mkl being required to be symmetric. Under g-variation S is required to be stationary with respect to variations of the metric tensor gij, the Gamma mkl being taken to be Christoffel symbols from the outset, whereas under P-variations the gij and Gamma mkl are initially regarded as mutually independent of S is required to be stationary with respect to independent variations of these quantities. The discussion is illustrated at length by examples in which the Lagrangian of S is one or another of a set of homogeneous or inhomogeneous quadratic invariants of the Riemann tensor.Keywords
This publication has 2 references indexed in Scilit:
- On functionally constant invariants of the Riemann tensorMathematical Proceedings of the Cambridge Philosophical Society, 1970
- Non-linear Lagrangians and Palatine's deviceMathematical Proceedings of the Cambridge Philosophical Society, 1960