Open AccessPosted Content
Complex manifolds with ample tangent bundles
TLDR
The complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces was proved in this article, where it was shown that if the global holomorphic sections of tangent bundle generate each fibre, then $M$ is a complex homogeneous manifold.Abstract:
Let $M$ be a close complex manifold and $TM$ its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then $M$ is a complex homogeneous manifold. Our proof depends on the complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces.read more
Citations
References
More filters
Posted Content
The entropy formula for the Ricci flow and its geometric applications
TL;DR: In this article, a monotonic expression for Ricci flow, valid in all dimensions and without curvature assumptions, is presented, interpreted as an entropy for a certain canonical ensemble.
Book ChapterDOI
Carnot-Carathéodory spaces seen from within
TL;DR: In this article, a local condition on curves is defined for a smooth manifold, where a subset H in the set of all piecewise smooth curves c in V is distinguished by local condition.
Journal ArticleDOI
Characterizations of complex projective spaces and hyperquadrics
TL;DR: In this article, the Ricci curvature of a Kdhler manifold has been characterized in terms of the first Chern class of a manifold, which is closely related to Ricci's curvature.
Journal ArticleDOI
The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature
TL;DR: Soit (X, h) une variete de Kahler compacte a n dimensions de courbure bisectionnelle holomorphe non negative et soit ( X, h~) son espace de recouvrement universel Alors il existe des entiers non negatifs k, N 1,…, N l et des espaces symetriques hermitiens compacts ineductibles M 1,