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Hwang, Jun Muk
복소기하학 연구단
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Minimal Rational Curves and 1-Flat Irreducible G-Structures

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Title
Minimal Rational Curves and 1-Flat Irreducible G-Structures
Author(s)
Jun-Muk Hwang; Li, Qifeng
Publication Date
2022-04
Journal
Journal of Geometric Analysis, v.32, no.6
Publisher
Springer
Abstract
1-Flat irreducible G-structures, equivalently, irreducible G-structures admitting torsion-free affine connections, have been studied extensively in differential geometry, especially in connection with the theory of affine holonomy groups. We propose to study them in a setting in algebraic geometry, where they arise from varieties of minimal rational tangents (VMRT) associated to families of minimal rational curves on uniruled projective manifolds. We prove that such a structure is locally symmetric when the dimension of the uniruled projective manifold is at least 5. By the classification result of Merkulov and Schwachhöfer on irreducible affine holonomy, the problem is reduced to the case when the VMRT at a general point of the uniruled projective manifold is isomorphic to a subadjoint variety. In the latter situation, we prove a stronger result that, without the assumption of 1-flatness, the structure arising from VMRT is always locally flat. The proof employs the method of Cartan connections. An interesting feature is that Cartan connections are considered not for the G-structures themselves, but for certain geometric structures on the spaces of minimal rational curves.
URI
https://pr.ibs.re.kr/handle/8788114/12178
DOI
10.1007/s12220-022-00901-7
ISSN
1050-6926
Appears in Collections:
Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
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