An algebraic characterization of affine manifolds with g-stucture satisfying a homogeneity condition

$δ$-homogeneity in Finsler geometry and the positive curvature problem

In this paper, we explore the similarity between normal homogeneity and $δ$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $δ$-homogeneous Finsler space is $G$-$δ$-homo-geneous, for some suitably chosen connected quasi-compact $G$. So $δ$-homogeneous Finsler metrics can be defined by a bi-invariant singular metric on $G$ and submersion, just as normal homogeneous metrics, using a bi-invariant Finsler metric on $G$ instead. More careful analysis shows, in the space of all Finsler metrics on $G/H$, the subset of all $G$-$δ$-homogen…

关于齐性凯勒流形

On Homogeneous Kähler Manifolds

本文刻画了齐性凯勒结构对萨萨基安结构的推广程度，将萨萨基安几何扩展至非可定向接触结构，还可通过修改齐性条件包含余凯勒结构及其推广。

On $δ$-homogeneous Riemannian manifolds

We study in this paper previously defined by V.N. Berestovskii and C.P. Plaut $δ$-homogeneous spaces in the case of Riemannian manifolds. Every such manifold has non-negative sectional curvature. The universal covering of any $δ$-homogeneous Riemannian manifolds is itself $δ$-homogeneous. In turn, every simply connected Riemannian $δ$-homogeneous manifold is a direct metric product of an Euclidean space and compact simply connected indecomposable homogeneous manifolds; all factors in this product are itself $δ$-homogeneous. We find different characterizations of $δ$-homogeneous Riemannian spac…