Pseudo-Riemannian geometry calibrates optimal transportation

Pseudo-riemannian Geometry Calibrates Optimal Transportation

Given a transportation cost c : M M ! R, optimal maps minimize the total cost of moving masses from M to M . We …nd, explicitly, a pseudo-metric and a calibration form on M M such that the graph of an optimal map is a calibrated maximal submanifold. We de…ne the mass of space-like currents in spaces with inde…nite metrics.

Calibrating Optimal Transportation: a New Pseudo-riemannian Geometry

Given a transportation cost c : M × M̄ → R, optimal maps minimize the total cost of moving masses from M to M̄ . We find a pseudo-metric and a calibration form on M × M̄ such that the graph of an optimal map is a calibrated maximal submanifold. We define the mass of space-like currents in spaces with indefinite metrics.

1 Pseudo - Riemannian Geometry

Generalized pseudo-Riemannian geometry

Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fun...

Dimensional curvature identities on pseudo-Riemannian geometry

For a fixed n ∈ N, the curvature tensor of a pseudo-Riemannian metric, as well as its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less or equal than n. In this paper, we re-elaborate recent results by Gilkey-Park-Sekigawa regarding these p-covariant curvature identities, for p = 0, 2. To this end, we use the classical theory of natural operations, th...