Abstract

In this article, we have considered the Finsler space \(F^{n}\,(n>2)\) with a Generalized Matsumoto metric and found the necessary and sufficient criteria for it to be of Douglas type. We have also demonstrated the condition for the mentioned metric in Finsler space to become a Berwald space. The space is also projectively flat if it is a Berwald space.

中文翻译：

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广义松本芬斯勒空间的道格拉斯张量

摘要

在本文中，我们考虑了具有广义松本度量的芬斯勒空间\(F^{n}\,(n>2)\)，并找到了它是道格拉斯类型的充分必要条件。我们还证明了 Finsler 空间中的上述度量成为 Berwald 空间的条件。如果该空间是 Berwald 空间，那么该空间在投影上也是平坦的。