Sumio Yamada

The Einstein equation with time symmetry has been regarded as an elliptic variational problem, ever since H. Weyl in 1916 described the Schwarzschild metric using a single harmonic function. In a series of collaborative work with Marcus Khuri, Martin Reiris and Gilbert Weinstein, we constructed 5-dimensional gravitational solitons, and consequently 4-dimensional gravitational (Riemannian) instantons.  In 3+1 spacetime dimensions, there are known to be no nontrivial solitons (Lichnerowicz), and our new construction seems to indicate that the geometry of  higher dimensional Einstein spacetimes is geometrically more fertile.