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 $\overline{E}=(exp{\sigma }^v)E$, $\sigma \in C^{\infty }\left(M\right)$.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 $\overline{\alpha }=\alpha +\frac{1}{2}\sigma$.A new proof of M. Hashiguchi’s and Y. Ichijyō’s theo!

EUDML-ID : urn:eudml:doc:221563
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@article{702142,
     title = {On the conformal theory of Ichijy\=o manifolds},
     booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2002},
     pages = {[245]-254},
     mrnumber = {MR1972439},
     zbl = {1021.53048},
     url = {http://dml.mathdoc.fr/item/702142}
}

Szakál, Sz. On the conformal theory of Ichijyō manifolds, dans Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books,  (2002), pp. [245]-254. http://gdmltest.u-ga.fr/item/702142/