PIRSA:09050036

A Geodesic Equation for the Space of Sasakian metrics

Guan, P. (2009). A Geodesic Equation for the Space of Sasakian metrics. Perimeter Institute. https://pirsa.org/09050036

Guan, Pengfei. A Geodesic Equation for the Space of Sasakian metrics. Perimeter Institute, May. 09, 2009, https://pirsa.org/09050036 

          @misc{ pirsa_PIRSA:09050036,
            doi = {10.48660/09050036},
            url = {https://pirsa.org/09050036},
            author = {Guan, Pengfei},
            keywords = {},
            language = {en},
            title = {A Geodesic Equation for the Space of Sasakian metrics},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {may},
            note = {PIRSA:09050036 see, \url{https://pirsa.org}}
          }

Pengfei Guan McGill University

DOI 10.48660/09050036
Collection
Talk Type Conference

Abstract

"Sasakian geometry is often described as an odd dimensional counterparts of K\""ahler geometry. There is a natural Riemannian metric on the space of Sasakian metrics, which in turn gives a geodesic equation on this space. It can be viewed as parallel case of a well-known geodesic equation for the space of K\""ahler metrics. The equation is connected to some interesting geometric properties of Sasakian manifolds. It is a complicated complex Monge-Amp\`ere type involving gradient terms. We discuss the problem of existence and regularity of solutions of this type of equations. This is a joint work with Xi Zhang."