The metric in the superspace of Riemannian metrics and its relation to gravity
Abstract
Description
The space of all Riemannian metrics is infinite-dimensional. Nevertheless a great deal of usual Riemannian geometry can be carried over. The superspace of all Riemannian metrics shall be endowed with a class of Riemannian metrics; their curvature and invariance properties are discussed. Just one of this class has the property to bring the lagrangian of General Relativity into the form of a classical particle's motion. The signature of the superspace metric depends in a non-trivial manner on the signature of the original metric, we derive the corresponding formula. Our approach is a local one: the essence is a metric in the space of all symmetric rank-two tensors, and then the space becomes a warped product of the real line with an Einstein space.
10 pages, LaTeX, reprinted from Proc. Conf. Diff. Geom. Appl., Brno, Czechoslovakia 1989, WSPC Singapore, Eds. J. Janyska, D. Krupka
10 pages, LaTeX, reprinted from Proc. Conf. Diff. Geom. Appl., Brno, Czechoslovakia 1989, WSPC Singapore, Eds. J. Janyska, D. Krupka