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arXiv · 2407.16263

Characteristic conic connections and torsion-free principal connections

Jun-Muk Hwang·Qifeng Li
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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.

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Jun-Muk Hwang, Qifeng Li. 2024-07-23. Characteristic conic connections and torsion-free principal connections. https://arxiv.org/abs/2407.16263

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