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math.DG2025
Left invariant complex Finsler metrics on a complex Lie group
Xiyun Xu, Ming Xu
In this paper, we consider a left invariant complex Finsler metric on a complex Lie group. Using the technique of invariant frames, we prove the following properties for $(G,F)…
math.DG2025
A counter example for the Homogeneity Conjecture
Ming Xu, Shaoqiang Deng
We construct a counter example to show that the Homogeneity Conjecture, first proposed by J.A. Wolf in 1962, is not true. To be precise, we prove that on the Lie group Sp(2), there…
math.DG2025
Very standard homogeneous Finsler manifolds with positive flag curvature
Xiyun Xu, Ming Xu
In this paper, we consider a homogeneous manifold in which is a compact connected simply connected simple Lie group and is a closed connected subgroup of . We defi…