Lorenzo Foscolo, Stony Brook University
“New Einstein metrics on the 6-sphere and the product of two 3-spheres, nearly K ̈ahler 6-manifolds and G2 cones”
At least since 1947 it has been known that octonionic multiplication induces an almost complex structure on the 6-sphere. This almost complex structure is intimately related to the standard torsion- free G2 structure on Euclidean 7-space, seen as the cone over the round sphere. In the talk we will look more in general at the class of almost complex 6-manifolds, so-called nearly Kh ̈ler 6-manifolds, which are the cross-sections of Riemannian cones with G2 holonomy. Besides their almost complex structure, nearly K ̈ahler 6-manifolds carry a rich geometric structure. For example, every nearly K ̈ahler 6-manifold is equipped with an Einstein metric.
A long-standing problem in almost complex geometry has been the question of existence of complete inhomogeneous nearly K ̈ahler 6-manifolds. We resolve this problem by proving the existence of an exotic (inhomogeneous) nearly K ̈ahler structure on the 6-sphere and on the product of two 3-spheres. The talk is based on joint work with Mark Haskins (Imperial College London).
M3 3103
Refreshments will be served in M3 3103 at 3:30 pm. Everyone is welcome to attend.