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Finsler spaces from conformal \(\beta\)-change. (English) Zbl 1499.53110

Summary: We have considered the conformal \(\beta\)-change of the Finsler metric given by \(L(x,y)\to\overline{L}(x,y)=e^{\sigma(x)}f(L(x,y), \beta(x,y))\), where \(\sigma(x)\) is a function of \(x\), \(\beta(x,y)= b_i(x)y^i\) is a 1-form on the underlying manifold \(M^n\), and \(f(L(x,y), \beta(x,y))\) is a homogeneous function of degree one in \(L\) and \(\beta\). Let \(F^n\) and \(\overline{F}^n\) denote Finsler spaces with metric functions \(L\) and \(\overline{L}\) respectively. It has been investigated how \(S_3\)-likeness and \(S_4\)-likeness of \(F^n\) are linked with corresponding properties of \(\overline{F}^n\). Further, necessary and sufficient conditions for a Killing vector field of \(F^n\) to be a vector field of the same kind in \(\overline{F}^n\) have been obtained.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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