On a transformation associated with sets of \(n\)-fundamental forms of Finsler hypersurfaces (Q1195016)
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scientific article; zbMATH DE number 68884
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a transformation associated with sets of \(n\)-fundamental forms of Finsler hypersurfaces |
scientific article; zbMATH DE number 68884 |
Statements
On a transformation associated with sets of \(n\)-fundamental forms of Finsler hypersurfaces (English)
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13 October 1992
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In the Finsler spaces \((M^ n,L)\) and \((M^ n,\;^*L)\), \(^*L=f(L,\beta)\), \(\beta=b_ i(x,y)y^ i\), the relation between tensors \(S_ h{^ i}_{jk}\) and \(S^*{}_ h{^ i}_{jk}\), with respect to the Cartan's connection is given. The relations between the \(r\)-th fundamental forms [defined by \textit{H. Rund}, Tensor, New Ser. 22, 163-173 (1971; Zbl 0203.241)]\ of the \((M_ x^{n-1},\bar g_ x)\) and \((M^{n-1}_ x, {^*\bar g}_ x)\) are obtained.
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Cartan's connection
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