We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not of Kahler ...

Document(s)

Title

We extend our previous classification [DW4] of superpotentials of "scalar curvature type" for the cohomogeneity one Ricci-flat equations. We now consider the case not covered in [DW4], i.e., when some weight vector of the superpotential lies outside ...

We apply techniques of Painlevé-Kowalewski analysis to a Hamiltonian system arising from symmetry reduction of the Ricci-flat Einstein equations. In the case of doubly warped product metrics on a product of two Einstein manifolds over an interval, we...

We apply Painlevé analysis to the Ricci-flat Einstein equations for a warped product with an arbitrary number of factors. We find that, as in the situation of the two factors examined [J. Geom. Phys. 38, 183-206 (2001)], the cases when the total dime...

We apply techniques of Painlevé-Kowalewski analysis to certain ODE reductions of the Ricci-flat equations. We particularly focus on two examples when the hypersurface is an Aloff-Wallach space or a circle bundle over a Fano product. © 2003 American I...

We give an elementary treatment of the existence of complete Kähler–Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n + 1)-sphere.

We produce explicit solutions for some cases of the cohomogeneity one Einstein equations by finding generalised first integrals of the Hamiltonian form of these equations. The resulting manifolds have dimension 10, 11 and 27.

We discuss various aspects of moment map geometry in symplectic and hyperKähler geometry. In particular, we classify complete hyperKähler manifolds of dimension 4n with a tri-Hamiltonian action of a torus of dimension n, without any assumption on the...

We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not of Kahler ...