Translator Disclaimer
Open Access
VOL. 48 | 2007 Ehresmann connections, metrics and good metric derivatives
Rezső L. Lovas, Johanna Pék, József Szilasi

Editor(s) Sorin V. Sabau, Hideo Shimada


In this survey we approach some aspects of tangent bundle geometry from a new viewpoint. After an outline of our main tools, i.e., the pull-back bundle formalism, we give an overview of Ehresmann connections and covariant derivatives in the pull-back bundle of a tangent bundle over itself. Then we define and characterize some special classes of generalized metrics. By a generalized metric we shall mean a pseudo-Riemannian metric tensor in our pull-back bundle. The main new results are contained in Section 5. We shall say, informally, that a metric covariant derivative is 'good' if it is related in a natural way to an Ehresmann connection determined by the metric alone. We shall find a family of good metric derivatives for the so-called weakly normal Moór–Vanstone metrics and a distinguished good metric derivative for a certain class of Miron metrics.


Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1144.53033
MathSciNet: MR2389258

Digital Object Identifier: 10.2969/aspm/04810263

Rights: Copyright © 2007 Mathematical Society of Japan


Back to Top