论文标题
特殊左不变的圆锥鳍指标和均匀的圆锥形兰斯伯格问题二维问题
Special left invariant conic Finsler metrics and homogeneous conic Landsberg Problem in two dimension
论文作者
论文摘要
在本文中，我们在二维非亚洲谎言组$ g $上研究了左锥鳍指标，没有任何地方消失的喷雾矢量场，并分别对满足恒定曲率条件，兰德斯伯格条件或伯瓦尔德条件的持续消失。我们证明，$ g $上的任何左圆锥形Landsberg公制都必须是Berwald。这一发现使我们能够提出一个同质的锥形兰斯伯格猜想，该发现猜测每个均匀的锥形兰斯伯格指标都是伯瓦尔德，并证明了这是二维案例。
In this paper, we study left invariant conic Finsler metrics on the 2-dimensional non-Abelian Lie group $G$ with nowhere vanishing spray vector fields, and classify those satisfying the constant curvature condition, the Landsberg condition or the Berwald condition respectively. We prove that any left invariant conic Landsberg metric on $G$ must be Berwald. This discovery enable us to propose a homogeneous conic Landsberg Conjecture, which guesses that every homogeneous conic Landsberg metric is Berwald, and prove the 2-dimensional case for it.
