Special geometries associated to quaternion-Kahler 8-manifolds

          @misc{ pirsa_PIRSA:09050030,
            doi = {10.48660/09050030},
            url = {https://pirsa.org/09050030},
            author = {Gambioli, Andrea},
            keywords = {},
            language = {en},
            title = {Special geometries associated to quaternion-Kahler 8-manifolds},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {may},
            note = {PIRSA:09050030 see, \url{https://pirsa.org}}
          }
          

Abstract

In this talk we will discuss the (local) construction of a calibrated G_2 structure on the 7-dimensional quotient of an 8-dimensional quaternion-Kahler (QK) manifold M under the action of a group S^1 of isometries. The idea is to construct explicitly a 3-form of type G_2, using the data associated to the S^1 action and to the QK structure on M. In the same spirit, we can consider the level sets of the QK moment-map square-norm function on M, and again take the S^1 quotient: we will discuss in this case the construction of half-flat metrics in dimension 6, under suitable circumstances. This talk is based on a joint work with F. Lonegro, Y. Nagatomo and S. Salamon, still in progress.