Ricci Flow Gravity

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar ...

Ricci Flow, Quantum Mechanics and Gravity

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 quantum mechanics with a complex d–dimensional Hilbert space, the Lie group SU(d) represents classical canonical transformations on the projective space CP of quantum states. Let R stand for the Ricci flo...

Ricci Lower Bound for Kähler–ricci Flow

Generalized Discrete Ricci Flow

Surface Ricci flow is a powerful tool to design Riemannian metrics by user defined curvatures. Discrete surface Ricci flow has been broadly applied for surface parameterization, shape analysis, and computational topology. Conventional discrete Ricci flow has limitations. For meshes with low quality triangulations, if high conformality is required, the flow may get stuck at the local optimum of ...

Nonholonomic Ricci Flows: Exact Solutions and Gravity

In a number of physically important cases, the nonholonomically (nonintegrable) constrained Ricci flows can be modelled by exact solutions of Einstein equations with nonhomogeneous (anisotropic) cosmological constants. We develop two geometric methods for constructing such solutions: The first approach applies the formalism of nonholonomic frame deformations when the gravitational evolution and...