HIRACHI Kengo

Professor

Department of Mathematics (UG), Graduate School of Mathematical Sciences

Current Research

I am studying the geometry of conformal and CR manifolds from the unified point of view of Parabolic geometry. To construct geometric invariants and invariant differential operators on these manifolds, I use the method of embedding them into higher dimensional Einstein manifolds; the invariants are then obtained from the asymptotic behavior of the Einstein metrics. This approach has good applications, e.g., for the asymptotic expansion of the Bergman kernel.

Keywords

CR manifold, coformal manifold, invariant differential operators, Bergman kernel, Einstein Equation