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ON THE PROBLEM OF NON-BERWALDIAN LANDSBERG SPACES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 102 / Issue 2 / October 2020
- Published online by Cambridge University Press:
- 08 January 2020, pp. 331-341
- Print publication:
- October 2020
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- Article
- Export citation
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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.
