| Title:
|
On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach (English) |
| Author:
|
Vincze, Csaba |
| Author:
|
Khoshdani, Tahere Reza |
| Author:
|
Gilani, Sareh Mehdi Zadeh |
| Author:
|
Oláh, Márk |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
27 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
51-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Finsler spaces |
| Keyword:
|
Generalized Berwalds spaces |
| Keyword:
|
Intrinsic Geometry |
| MSC:
|
53C60 |
| MSC:
|
58B20 |
| idZBL:
|
Zbl 1469.53117 |
| idMR:
|
MR3977477 |
| . |
| Date available:
|
2019-06-28T14:49:58Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147768 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Berwald, L.: Über zweidimensionale allgemeine metrische Räume.Journal für die reine und angewandte Mathematik, 156, 1927, 191-222, MR 1581095 |
| Reference:
|
[4] Berwald, L.: On Finsler and Cartan geometries. III: two-dimensional Finsler spaces with rectilinear extremals.Annals of Mathematics, 1941, 84-112, MR 0003992, 10.2307/1968989 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Shen, Z.: Differential Geometry of Spray and Finsler Spaces.2001, Kluwer Academic Publishers, Zbl 1009.53004, MR 1967666 |
| Reference:
|
[8] Vattamány, Sz., Vincze, Cs.: Two-dimensional Landsberg manifolds with vanishing Douglas tensor.Annales Univ. Sci. Budapest, 44, 2001, 11-26, MR 1917696 |
| Reference:
|
[9] Vattamány, Sz., Vincze, Cs.: On a new geometrical derivation of two-dimensional Finsler manifolds with constant main scalar.Period. Math. Hungar., 48, 1--2, 2004, 61-67, MR 2077686, 10.1023/B:MAHU.0000038966.20644.e8 |
| Reference:
|
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| Reference:
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[11] Vincze, Cs.: On a scale function for testing the conformality of Finsler manifolds to a Berwald manifold.Journal of Geometry and Physics, 54, 4, 2005, 454-475, Elsevier, MR 2144712, 10.1016/j.geomphys.2004.11.004 |
| Reference:
|
[12] Vincze, Cs.: On Berwald and Wagner manifolds.Acta Math. Acad. Paedagog. Nyházi.(NS), 24, 2008, 169-178, MR 2430244 |
| Reference:
|
[13] Vincze, Cs.: On generalized Berwald manifolds with semi-symmetric compatible linear connections.Publ. Math. Debrecen, 83, 4, 2013, 741-755, MR 3150840, 10.5486/PMD.2014.5750 |
| Reference:
|
[14] Vincze, Cs.: On a special type of generalized Berwald manifolds: semi-symmetric linear connections preserving the Finslerian length of tangent vectors.European Journal of Mathematics, 3, 4, 2017, 1098-1171, Springer, MR 3736800, 10.1007/s40879-017-0153-5 |
| Reference:
|
[15] Vincze, Cs.: Lazy orbits: an optimization problem on the sphere.Journal of Geometry and Physics, 124, 2018, 180-198, Elsevier, MR 3754505, 10.1016/j.geomphys.2017.10.018 |
| Reference:
|
[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, |
| Reference:
|
[17] Wagner, V.: On generalized Berwald spaces.CR (Doklady) Acad. Sci. URSS (NS), 39, 1943, 3-5, MR 0009147 |
| . |
