This paper introduces new non-Riemannian quantities and classes of Finsler metrics. The study focuses on the class of Generalized Douglas Weyl GDW-metrics, which is contained in the class of Finsler metrics. The paper constructs the new sub-classes of GDW-metrics and presents illustrative examples.
1. PL. Antonelli and RS. Ingarden and M. Matsumoto, The Theorey of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer Academic Publishers, 1993.
2. H. Akbar-Zadeh, Sur les espaces de Finsler ´a courbures sectionnelles constantes, Bulletins de ´lAcad´emie Royale de Belgique, 5e S´erie - Tome LXXXIV, 10(1988), 281-322.
3. S. B´acs´o and I. Papp, A note on generalized Douglas space, Periodica Mathematica Hungarica, 48(2004), 181-184.
4. D. Bao and Z. Shen, Finsler metrics of constant positive curvature on the Lie group S3, Journal of London Mathematics Society, 66(2002), 453-467.
5. X. Cheng and Z. Shen, On Douglas metrics, Publ. Math. Debrecen. 66 3-4(2005), 503- 512.
6. X. Cheng and Z. Shen, Randers metrics with special curvature properties, Osaka Journal of Mathematics, 40 (2003), 87-101.
7. J. Douglas, The general geometry of paths, Annals of Mathematics, 29(1927-28), 143-168.
8. B. Najafi and B. Bidabad and A. Tayebi, On R-quadratic Finsler metrics, Iranian Journal of Science and Technology, Transaction A, Science 32 (2008), 439-443.
9. B. Najafi and A. Tayebi, A new quantity in Finsler geometry, Comptes Rendus Mathematique. 349(1) (2011), 81-83. On non-Riemannian quantities in Finsler geometry 73.
10. N. Sadeghzadeh, Beyond the Generalized Douglas-Weyl sapaces, Publ. Math. Debrecen. Submitted.
11. N. Sadeghzadeh, Generalized Berwald Projective Weyl (GBWf) metrics, Submitted.
12. Z. Shen, Landsberg curvature, S-curvature, and Riemann curvature, in A Sampler of Finsler Geometry, Mathematical Sciences Research Institute Publications, 50. Cambridge University Press, Cambridge, (2004), 303-355.
13. Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001.
14. Z. Szab´o, Ein Finslerscher Raum ist gerade dann von skalarer Kru¨mmung, wennseine Weyl sche ProjectivKru¨mmung verschwindet, Acta Scientiarum Mathematicarum 39 (1977), 163-168.
15. H. Weyl, Zur Infinitesimal geometrie ; Einordnung der projektiven und der konformen Auffassung, G¨ottinger Nachrichten, (1921), 99-112.
16. G. Yang, On a class of singular Douglas and projectively flat Finsler metrics, Differ. Geom. Appl. 32(2014), 113-129.
Sadeghzadeh, N. (2023). On non-Riemannian quantities in Finsler geometry. Journal of Finsler Geometry and its Applications, 4(2), 64-73. doi: 10.22098/jfga.2023.13783.1105
MLA
Nasrin Sadeghzadeh. "On non-Riemannian quantities in Finsler geometry", Journal of Finsler Geometry and its Applications, 4, 2, 2023, 64-73. doi: 10.22098/jfga.2023.13783.1105
HARVARD
Sadeghzadeh, N. (2023). 'On non-Riemannian quantities in Finsler geometry', Journal of Finsler Geometry and its Applications, 4(2), pp. 64-73. doi: 10.22098/jfga.2023.13783.1105
VANCOUVER
Sadeghzadeh, N. On non-Riemannian quantities in Finsler geometry. Journal of Finsler Geometry and its Applications, 2023; 4(2): 64-73. doi: 10.22098/jfga.2023.13783.1105