Characteristic conic connections and torsion-free principal connections

Autor:	Hwang, Jun-Muk, Li, Qifeng
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.16263 Zobrazit plný text záznamu View this record from Arxiv