Dept Math & Stat UiT, Forskningsparken B459

31 Aug 2023 Wed

10:30-12:00

Jun-Muk Hwang (Center for Complex Geometry, Daejeon, South Korea)

"Characteristic conic connections and torsion-free principal connections"

Let Z be a complex submanifold in the complex projective space P^{n-1} and let G be its complex linear automorphism group in GL(n). We study the natural one-to-one correspondence between G-structures and Z-isotrivial cone structures, in particular, the relation between torsion tensors of principal connections on G-structures and characteristic conic connections on the corresponding cone structures. We formulate conditions on Z, under which the existence of a characteristic conic connection implies the existence of a torsion-free principal connection. These conditions hold for adjoint varieties of simple Lie algebras, excluding types A_k and C_k, k>2. Combined with the result of Merkulov and Schwachhofer on irreducible affine holonomies, this implies that when Z is such an adjoint variety, a Z-isotrivial cone structure with characteristic conic connection must be locally symmetric. This is a joint work with Qifeng Li.

14:00-15:00

Henrik Winther (UiT)

"Compact and Non-Compact Parabolic Space Forms"

Let G be a connected complex or real simple Lie group and P its parabolic subgroup. In the complex case, G/P is a compact Kahler manifold. In the real case, it is known that G/P is compact as long as the center Z(G) is finite. On the other hand, there are no guarantees about compactness when this fails. We give a classification of all groups G and parabolic subgroups P=P_I for which the universal space form \widetilde{G/P} is non-compact. Interestingly, the set of such groups turns out to be a proper subset of the groups which admit infinite center. Joint work with Boris Kruglikov.