Shukla, H. S.; Mishra, Neelam; Shukla, Vivek Finsler spaces from conformal \(\beta\)-change. (English) Zbl 1499.53110 J. Rajasthan Acad. Phys. Sci. 20, No. 1-2, 37-48 (2021). 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) Keywords:Finsler metric; conformal \(\beta\)-change; \(S_3\)-like Finsler space; \(S_4\)-like Finsler space; \(v\)-curvature tensor; Killing vector field PDFBibTeX XMLCite \textit{H. S. Shukla} et al., J. Rajasthan Acad. Phys. Sci. 20, No. 1--2, 37--48 (2021; Zbl 1499.53110) Full Text: Link