On generalized Finsler metric \(LL_{ij}-\alpha L_ iL_ j\) (Q1263092)
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scientific article; zbMATH DE number 4126213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On generalized Finsler metric \(LL_{ij}-\alpha L_ iL_ j\) |
scientific article; zbMATH DE number 4126213 |
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On generalized Finsler metric \(LL_{ij}-\alpha L_ iL_ j\) (English)
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1988
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The author considers a Finsler space \(F^ n=(M,L(x,y))\) with a kind of generalized Finsler metric (GFM): \[ (1)\quad g_{ij}=LL_{ij}-\alpha L_ iL_ j, \] where \(L_ i=\partial L/\partial y^ i\), \(L_{ij}=dL_ i/\partial y^ j\) and \(\alpha =\alpha (x,y)\) is a scalar. He investigates the properties of the metric (1). It is shown that this GFM has similar properties to those of the usual Finsler metric. Moreover, he obtains a Finsler connection for GFM: \(LL_{ij}- \alpha L_ iL_ j\).
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Finsler space
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generalized Finsler metric
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