This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.
Almost positive curvature on $T^1\mathbb{K}P^n$ and other manifolds
Generalized P-Reducible $(α, β)$-Metrics with Vanishing S-curvature
$G_2$-instantons on noncompact $G_2$-manifolds: results and open problems
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