Minkowski空间的等价性定理及在Finsler几何的应用

首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的Landsberg空间为Berwald空间,这些条件可以是具有闭的Cartan型形式,S曲率为零或平均Berwald曲率为零.     

Cubic Form Methods and Relative Tchebychev Hypersurfaces

We introduce the concept of a relative Tchebychev hypersurface which extends that of affine spheres in equiaffine geometry and also that of centroaffine Tchebychev hypersurfaces and give partial local and global classifications for this new class. Our tools concern a new operator and interesting properties of the traceless part of the cubic form.