A Ferrand-Obata theorem for rank one parabolic geometries

关于共形向量场的局部洛伦兹 - 费朗 - 奥巴塔定理

A local Lorentzian Ferrand-Obata theorem for conformal vector fields

研究闭实解析洛伦兹流形上共形向量场，通过改进局部范式等方法，证明其流局部等距或度量处处共形平坦，此为洛伦兹 - 利希纳罗维茨猜想的局部版本。

C-projective geometry

We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kaehler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kaehler metrics underlying a given c-projective structure has many ramifications, which we explore in depth. As a consequence of this analysis, we prove the Yano-Obata conjecture for complete Kaehler manifold…