A mechanics for the Ricci flow (2008)
Abraham, S., De Cordoba, P. Fernandez, Isidro, J. M., Santander, J. L. G.
We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns...
The Ricci flow on Riemann surfaces (2008)
Abraham, S., De Cordoba, P. Fernandez, Isidro, J. M., Santander, J. L. G.
We establish a 1-to-1 relation between metrics on compact Riemann surfaces without boundary, and mechanical systems having those surfaces as configuration spaces.
A note on the quantum-mechanical Ricci flow (2008)
Isidro, J. M., Santander, J. L. G., De Cordoba, P. Fernandez
We obtain Schroedinger quantum mechanics from Perelman's functional and from the Ricci flow equations of a conformally flat Riemannian metric on a closed 2-dimensional configuration space. We explore...
Ricci flow, quantum mechanics and gravity (2008)
Isidro, J. M., Santander, J. L. G., De Cordoba, P. Fernandez
It has been argued that, underlying any given quantum-mechanical model, there exists at least one deterministic system that reproduces, after prequantisation, the given quantum dynamics. For a...