On the conformal theory of Ichijyō manifolds

Szakál, Sz.

Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books, (2002), p. [245]-254 / Harvested from

Résumé

Some special linear connection introduced in the Finsler space by Ichijyō has the property that the curvature tensors under conformal changes remain invariant. Two Ichijyō manifolds $(M,E,\nabla )$ and $(M,\overline{E},\overline{\nabla })$ are said to be conformally equivalent if $\overline{E}= (\exp \sigma ^v)E$, $\sigma \in C^\infty (M)$.It is proved, that in this case, the following assertions are equivalent: 1. $\sigma $ is constant, 2. $h_\nabla = h_{\overline{\nabla }}$, 3. $S_{\nabla }= S_{\overline{\nabla }}$, 4. $t_\nabla = t_{\overline{\nabla }}$.It is also proved (when the above conditions are satisfied) that1. If $(M,E,\nabla )$ is a generalized Berwald manifold, then $(M,\overline{E},\overline{\nabla })$ is also a generalized Berwald manifold.2. If $(M,E,\nabla )$ is a Wagner manifold, then $(M,\overline{E},\overline{\nabla })$ is also a Wagner manifold with $\overline{\alpha }= \alpha +{1\over 2} \sigma $.A new proof of M. Hashiguchi’s and Y. Ichijyō’s theo!

Détail

MR MR1972439 | Zbl 1021.53048

EUDML-ID : urn:eudml:doc:221563
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