Wolfram Alpha:
Search by keyword:
Astronomy
-
-
-
-
Chemistry
-
-
-
-
Classical Mechanics
-
Classical Physics
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Climate Change
-
Cosmology
-
-
.-
-
-
-
-
-
-
-
-
-
-
-
Finance and Accounting
-
-
-
-
-
-
-
-
-
Game Theory
-
General Relativity
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Group Theory
-
-
-
-
-
-
Lagrangian and Hamiltonian Mechanics
-
-
-
-
-
-
Macroeconomics
-
-
-
Mathematics
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Mathjax
-
Microeconomics
-
Nuclear Physics
-
-
Particle Physics
-
-
-
-
-
-
-
Probability and Statistics
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Programming and Computer Science
-
Hashing .
-
-
-
-
-
Quantitative Methods for Business
-
Quantum Computing
-
-
-
Quantum Field Theory
-
-
-
-
-
Quantum Mechanics
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Semiconductor Reliability
-
Solid State Electronics
-
-
-
-
-
Special Relativity
-
-
-
-
-
-
-
-
-
-
-
-
Statistical Mechanics
-
-
-
String Theory
-
-
-
-
-
-
Superconductivity
-
-
-
-
-
-
Supersymmetry (SUSY) and Grand Unified Theory (GUT)
-
-
-
-
-
The Standard Model
-
-
-
-
-
-
-
-
-
-
Topology
-
Units, Constants and Useful Formulas
-
Last modified: December 4, 2021 ✓
Ricci Flow
----------
For a Riemannian manifold the RICCI FLOW is a partial differential
equation that evolves the metric tensor over 'time'. It is analogous
to the diffusion of heat.
∂gμν(t)/∂t = -2Rμν(gμν(t))
The idea is to smooth out irregularities in the metric and make the
geometry of the manifold more symmetric. Informally, it can be
considered as the process of stretching the metric in directions of
negative Ricci curvature, and contracting the metric in directions
of positive Ricci curvature thereby increasing or decreasing the
distance between points on the manifold. The greater the curvature,
the faster the stretching or contracting. Changing the distances
also impacts the angle and area. However, in 2 dimensions the
Ricci flow is conformal meaning that angles do not change with
the flow.