On the conformal theory of Ichijyō manifolds

Szakál, Sz.. "On the conformal theory of Ichijyō manifolds." Proceedings of the 21st Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2002. [245]-254. <http://eudml.org/doc/221563>.

@inProceedings{Szakál2002,
abstract = {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!},
author = {Szakál, Sz.},
booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[245]-254},
publisher = {Circolo Matematico di Palermo},
title = {On the conformal theory of Ichijyō manifolds},
url = {http://eudml.org/doc/221563},
year = {2002},
}

TY - CLSWK
AU - Szakál, Sz.
TI - On the conformal theory of Ichijyō manifolds
T2 - Proceedings of the 21st Winter School "Geometry and Physics"
PY - 2002
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [245]
EP - 254
AB - 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!
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221563
ER -