Abstract
The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lies in the fact that this class of tensors includes the energy-momentum and Ricci tensors. Moreover, all curvature collineations are necessarily Ricci collineations. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra but also, in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Stefani H, Kramer D, MacCallum M, Hoenselaers C and Herlt E, Exact Solutions of Einstein’s Field Equations (Cambridge, Cambridge University Press) 2003; Yano K, The theory of Lie derivatives and its applications, (Amsterdam, North-Holland) 1955; Hall, G S, J Math Phys 31 1198 (1990); Hall, G S and Lonie, D P, Class Quantum Grav 12 1007 (1995)
Bokhari A H and Qadir A, J Math Phys 34 3543 (1993); Melfo A, Nuez L, Percoco U and Villalba V M, J Math Phys 33 2258 (1992); Carot, J, da Costa J and Vaz E G L R, J Math Phys 35 4832 (1994)
Hall, G S and da Costa, J, J Math Phys 32 2848 and 2854 (1991)
Llosa J, “ Matter and Ricci collineations”, arXiv:1302.3048
Godbillon C, Gometrie Diffrentielle et Mcanique analytique, (Paris; Hermann) 1969
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Llosa, J. (2014). Matter and Ricci Collineations. In: García-Parrado, A., Mena, F., Moura, F., Vaz, E. (eds) Progress in Mathematical Relativity, Gravitation and Cosmology. Springer Proceedings in Mathematics & Statistics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40157-2_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-40157-2_42
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40156-5
Online ISBN: 978-3-642-40157-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)