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Homogeneous Einstein Finsler metrics on $(4n+3)$-dimensional spheres
we discuss a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere.
We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ among this class.
Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain
the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.