| publication name | On the problem of non Berwaldian Landsberg spaces |
|---|---|
| Authors | Salah Elgendi |
| year | 2020 |
| keywords | sprays; Berwlad metrics; Landsberg metrics |
| journal | Bulletin of the Australian Mathematical Society |
| volume | 102 |
| issue | 2 |
| pages | 331-341 |
| publisher | Cambridge University Press |
| Local/International | International |
| Paper Link | https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/on-the-problem-of-nonberwaldian-landsberg-spaces/EC69D21F92C1D2EBCB77E1CFD34E6169 |
| Full paper | download |
| Supplementary materials | Not Available |
Abstract
We study the long-standing problem of the existence of non-Berwaldian Landsberg spaces from the perspective of conformal transformations. We calculate the Berwald and Landsberg tensors in terms of the T-tensor and show that there are Landsberg spaces with nonvanishing T-tensor. We give a necessary condition for a Landsberg space to be Berwaldian. We find conditions under which the Landsberg spaces cannot be Berwaldian and give examples of (y-local) non-Berwaldian Landsberg spaces