TY - JOUR
ID - 4498
TI - On generalized Berwald manifolds: extremal compatible linear connections, special metrics and low dimensional spaces
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Vincze, Csaba
AD - Department of Geometry, Faculty of Science and Technology, University of Debrecen, Debrecen, Hungary
Y1 - 2021
PY - 2021
VL - 2
IS - 2
SP - 213
EP - 237
KW - Averaging
KW - Riemann-Finsler Geometry
KW - Generalized Berwald manifolds
DO - 10.22060/ajmc.2021.20348.1063
N2 - The notion of generalized Berwald manifolds goes back to V. Wagner [60]. They are Finsler manifolds admitting linear connections on the base manifold such that the parallel transports preserve the Finslerian length of tangent vectors (compatibility condition). Presenting a panoramic view of the general theory we are going to summarize some special problems and results. Spaces of special metrics are of special interest in the generalized Berwald manifold theory. We discuss the case of generalized Berwald Randers metrics, Finsler surfaces and Finsler manifolds of dimension three. To provide the unicity of the compatible linear connection we are looking for, we introduce the notion of the extremal compatible linear connection minimizing the norm of the torsion tensor point by point. The mathematical formulation is given in terms of a conditional extremum problem for checking the existence of compatible linear connections in general. Explicite computations are presented in the special case of generalized Berwald Randers metrics.
UR - https://ajmc.aut.ac.ir/article_4498.html
L1 - https://ajmc.aut.ac.ir/article_4498_73723601b0f336bcbb0c09b6e868e1e1.pdf
ER -