Methoden der Riemannschen Geometrie in der Finslergeometrie

• Antragsteller: Professor Dr. Vladimir Matveev
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2016 bis 2022
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 318916629

• Erstellungsjahr: 2022

Zusammenfassung der Projektergebnisse

We view the following four results as main scientific outcome of the project. • We have shown that a generic Finsler metric has infinite-dimensional holonomy group. • We have proved the Landsberg Unicorn conjecture under the additional assumption that for every point the restriction of the Finsler metric to the point is symmetric with respect to the standard action of SO(n - 1). • We have proved that for generic Finlser metric the holonomy group is infinite-dimensional. • We have described all 2-dimensional Finsler metrics admitting 3 projective vector fields. • We have shown that on a closed surface of negative Euler characteristic two projectively equivalent Finsler metrics are trivially projectively equivalent.

Projektbezogene Publikationen (Auswahl)

• Differentiability of projective transformations in dimension 2. Adv. Geom. 20 (2020), no. 4, 553-557
  Lang, Julius
  (Siehe online unter https://doi.org/10.1515/advgeom-2019-0023)
• Finsler metrics on surfaces admitting three projective vector fields. Differential Geom. Appl. 69 (2020), 101590, 13 pp
  Lang, Julius
  (Siehe online unter https://doi.org/10.1016/j.difgeo.2019.101590)
• On Finsler surfaces that are both Douglas and generalized Berwald. Publ. Math. Debrecen 97 (2020), no. 3-4, 381-391
  Bartelmess, Nina; Lang, Julius
  (Siehe online unter https://doi.org/10.5486/PMD.2020.8784)
• Almost all Finsler metrics have infinite dimensional holonomy group. J. Geom. Anal. 31 (2021), no. 6, 6067-6079
  Hubicska, B.; Matveev, V. S.; Muzsnay, Z.
  (Siehe online unter https://doi.org/10.1007/s12220-020-00517-9)
• Conformally related Douglas metrics in dimension two are Randers. Arch. Math. (Basel) 116 (2021), no. 2, 221-231
  Matveev, Vladimir S., Saberali, Samaneh
  (Siehe online unter https://doi.org/10.1007/s00013-020-01533-5)
• Proof of Laugwitz Conjecture and Landsberg Unicorn Conjecture for Minkowski norms with SO(k) x SO(n-k)-symmetry. Canadian Journal of Mathematics
  Xu, Ming, Matveev, Vladimir S.
  (Siehe online unter https://doi.org/10.4153/S0008414X21000304)
• Projectively equivalent Finsler metrics on surfaces of negative Euler characteristic. J. Topol. Anal. 14 (2022), no. 1, 287-296
  Lang, Julius
  (Siehe online unter https://doi.org/10.1142/s1793525320500491)