RT Journal Article
T1 From the Fermi-Walker to the Cartan connection
A1 Lafuente López, Javier
A1 Salvador, Beatriz
AB Let M be a differentiable manifold and C ={e2org / a : M -> R } a Riemannian conformal structure on M. Given any regular curve in M, 7 : I -> M, there is a natural way of defining an operator, D/dt: £(7) -> £(7), the Fermi-Walkerconnection along 7, which only depends on the conformal structure C, and such that it coincides with the Fermi-Walker connection along 7 -in the classical sense- of anyg € C such that g("y'(t),y'(t)) = 1 Vt G I. This Fermi- Walker connection enables us to construct a lift-function Kb : T*M -> TbCO(M) for every b G CO(M), and p = n(b), n : CO(M) —> M being the usual projection. In some sense, Kb combines all the different lift-functions TPM -> T6CO(M) given by the Levi-Civita connections of the compatibles metrics g € C. But over all, Kb determines the conformal structure C over M, so that it may be used to know about the normal Cartan connection and the Weyl conformal curvature tensor.
PB Springer
SN 0009-725X
YR 2000
FD 2000
LK https://hdl.handle.net/20.500.14352/58340
UL https://hdl.handle.net/20.500.14352/58340
LA eng
NO B. O'Neill, Semi-Riemannian Geometry with applicatins to relativity. Academic Press Inc, 1983.Wfalter A. Poor, Differential Geometric structures. McGraw-Hill Book Company, 1981.S.-T. Yau R. Schoen, Lectures on Differential Geometry. International Press, 1994.H.Wu R.K.Sachs, General Relativity for Mathematicians. Springer-Verlag, 1977.J Lafontaine S. Gallot, D. Hulin, Riemannian Geometry. Springer-Verlag, 1993.J. A. Schouten, Ricci-Calculus. Springer-Verlag, 1954.S.Kobayashi, Transformation Groups in Differential Geometry. Springer-Verlag, 1972.K.Nomizu S.Kobayashi, Foundations of Differential Geometry. Interscience Publisher, 1963.S. Sternberg, Lectures on Differential Geometry. Prentice Hall Inc., 1964.S. Haperlin W. Greub, Connections, Curvature and Cohomology. Academic Press, 1973.Kentaro Yano, Integral formulas in Riemannian Geometry. Marcel Dekker Inc, 1970.
NO Jan Slovák and Martin Čadek (eds.): Proceedings of the 19th Winter School "Geometry and Physics". Circolo Matematico di Palermo, Palermo, 2000. Rendiconti del Circolo Matematico diPalermo, Serie II, Supplemento No. 63. pp. 149--156.
DS Docta Complutense
RD 2 may 2024