1. Characteristic conic connections and torsion-free principal connections
- Author
-
Hwang, Jun-Muk and Li, Qifeng
- Subjects
Mathematics - Differential Geometry ,Mathematics - Algebraic Geometry - Abstract
We study the relation between torsion tensors of principal connections on G-structures and characteristic conic connections on associated cone structures. We formulate sufficient conditions under which the existence of a characteristic conic connection implies the existence of a torsion-free principal connection. We verify these conditions for adjoint varieties of simple Lie algebras, excluding those of type $\textsf{A}_{\ell \neq 2}$ or $\textsf{C}_{\ell}$. As an application, we give a complete classification of the germs of minimal rational curves whose VMRT at a general point is such an adjoint variety: nontrivial ones come from lines on hyperplane sections of certain Grassmannians or minimal rational curves on wonderful group compactifications., Comment: To appear in Journal de Math\'ematiques Pures et Appliqu\'ees
- Published
- 2024