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ON THE PROBLEM OF NON-BERWALDIAN LANDSBERG SPACES
Bulletin of the Australian Mathematical Society ( IF 0.7 ) Pub Date : 2020-01-08 , DOI: 10.1017/s000497271900128x
S. G. ELGENDI

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.

中文翻译:

关于非伯瓦尔第兰兹伯格空间的问题

我们从保角变换的角度研究了长期存在的非 Berwaldian Landsberg 空间存在的问题。我们根据 T-张量计算 Berwald 张量和 Landsberg 张量,并表明存在具有非零 T-张量的 Landsberg 空间。我们给出了 Landsberg 空间成为 Berwaldian 的必要条件。我们找到了 Landsberg 空间不能是 Berwaldian 的条件,并给出了 ($y$-local) 非 Berwaldian Landsberg 空间。
更新日期:2020-01-08
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