On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach

Csaba Vincze; Tahere Reza Khoshdani; Sareh Mehdi Zadeh Gilani; Márk Oláh

Communications in Mathematics (2019)

  • Volume: 27, Issue: 1, page 51-68
  • ISSN: 1804-1388

Abstract

top
In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.

How to cite

top

Vincze, Csaba, et al. "On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach." Communications in Mathematics 27.1 (2019): 51-68. <http://eudml.org/doc/294492>.

@article{Vincze2019,
abstract = {In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.},
author = {Vincze, Csaba, Khoshdani, Tahere Reza, Gilani, Sareh Mehdi Zadeh, Oláh, Márk},
journal = {Communications in Mathematics},
keywords = {Finsler spaces; Generalized Berwalds spaces; Intrinsic Geometry},
language = {eng},
number = {1},
pages = {51-68},
publisher = {University of Ostrava},
title = {On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach},
url = {http://eudml.org/doc/294492},
volume = {27},
year = {2019},
}

TY - JOUR
AU - Vincze, Csaba
AU - Khoshdani, Tahere Reza
AU - Gilani, Sareh Mehdi Zadeh
AU - Oláh, Márk
TI - On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach
JO - Communications in Mathematics
PY - 2019
PB - University of Ostrava
VL - 27
IS - 1
SP - 51
EP - 68
AB - In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.
LA - eng
KW - Finsler spaces; Generalized Berwalds spaces; Intrinsic Geometry
UR - http://eudml.org/doc/294492
ER -

References

top
  1. Bao, D., 10.2969/aspm/04810019, Advanced Studies in Pure Mathematics, 48, 2007, 19-71, (2007) MR2389251DOI10.2969/aspm/04810019
  2. Bao, D., Chern, S.-S., Shen, Z., An Introduction to Riemann-Finsler geometry, 2000, Springer-Verlag, (2000) MR1747675
  3. Berwald, L., Über zweidimensionale allgemeine metrische Räume, Journal für die reine und angewandte Mathematik, 156, 1927, 191-222, (1927) MR1581095
  4. Berwald, L., 10.2307/1968989, Annals of Mathematics, 1941, 84-112, (1941) MR0003992DOI10.2307/1968989
  5. Hashiguchi, M., 10.1215/kjm/1250522956, J. Math. Kyoto Univ., 16, 1976, 25-50, (1976) MR0402642DOI10.1215/kjm/1250522956
  6. Matsumoto, M., Foundations of Finsler geometry and special Finsler spaces, 1986, Kaiseisha press, (1986) MR0858830
  7. Shen, Z., Differential Geometry of Spray and Finsler Spaces, 2001, Kluwer Academic Publishers, (2001) Zbl1009.53004MR1967666
  8. Vattamány, Sz., Vincze, Cs., Two-dimensional Landsberg manifolds with vanishing Douglas tensor, Annales Univ. Sci. Budapest, 44, 2001, 11-26, (2001) MR1917696
  9. Vattamány, Sz., Vincze, Cs., 10.1023/B:MAHU.0000038966.20644.e8, Period. Math. Hungar., 48, 1--2, 2004, 61-67, (2004) MR2077686DOI10.1023/B:MAHU.0000038966.20644.e8
  10. Vincze, Cs., A new proof of Szabó's theorem on the Riemann-metrizability of Berwald manifolds, Acta Math. Acad. Paedagog. Nyházi (NS), 21, 2, 2005, 199-204, (2005) MR2162616
  11. Vincze, Cs., 10.1016/j.geomphys.2004.11.004, Journal of Geometry and Physics, 54, 4, 2005, 454-475, Elsevier, (2005) MR2144712DOI10.1016/j.geomphys.2004.11.004
  12. Vincze, Cs., On Berwald and Wagner manifolds, Acta Math. Acad. Paedagog. Nyházi.(NS), 24, 2008, 169-178, (2008) MR2430244
  13. Vincze, Cs., 10.5486/PMD.2014.5750, Publ. Math. Debrecen, 83, 4, 2013, 741-755, (2013) MR3150840DOI10.5486/PMD.2014.5750
  14. Vincze, Cs., 10.1007/s40879-017-0153-5, European Journal of Mathematics, 3, 4, 2017, 1098-1171, Springer, (2017) MR3736800DOI10.1007/s40879-017-0153-5
  15. Vincze, Cs., 10.1016/j.geomphys.2017.10.018, Journal of Geometry and Physics, 124, 2018, 180-198, Elsevier, (2018) MR3754505DOI10.1016/j.geomphys.2017.10.018
  16. Vincze, Cs., Oláh, M., Alabdulsada, Layth M., On the divergence representation of the Gauss curvature of Riemannian surfaces and its applications, Rendiconti del Circolo Matematico di Palermo Series 2, 2018, 1-13, Springer, (2018) 
  17. Wagner, V., On generalized Berwald spaces, CR (Doklady) Acad. Sci. URSS (NS), 39, 1943, 3-5, (1943) MR0009147

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.