Geodesics on spaces of almost hermitian structures
A natural metric on the space of all almost hermitian structures on a given manifold is investigated.
math.DG↗
arXiv subjects
Olga Gil-Medrano
Publications and source records attributed to Olga Gil-Medrano.
Pseudoriemannian metrics on spaces of bilinear structures
The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation explicitly. Each space of pseudo Riemannian metrics with fixed signature is a geodesically closed submanifold. The space of non degenerate 2-forms is also a geodesically closed submanifold. Then we show that, if we fix a distribution on $M$, the space of all Riemannia metrics splits as the product of three spaces which are everywhere mutually orthogonal, for the usual metric. We investigate this situation in detail.
math.DG↗
The Riemannian manifold of all Riemannian metrics
The space of all Riemannian metrics on a smooth second countable finite dimensional manifold is itself a smooth manifold modeled on the space of symmetric (0,2)-tensor fields with compact support. It carries a canonical Riemannian metric which is invariant under the action of the diffeomorphism group. We determine its geodesics, exponential mapping, curvature, and Jacobi fields in a very explicit manner.
math.DG↗