Metric Equivalence Problem
- 1. Find a complete system of invariants, or
- 2. decide when two Metrics differ only by a coordinatetransformation.
and 
, does thereexist a coordinate transformation from one to the other?'' Christoffel and Lipschitz (1870) showed howto decide this question for two Riemannian Metrics. The solution by E. Cartan requirescomputation of the 10th order Covariant Derivatives. The demonstration was simplified byA. Karlhede using the Tetrad formalism so that only seventh order Covariant Derivatives need be computed. However, in many common cases, the first or second-order Derivativesare Sufficient to answer the question.
References
Karlhede, A. and Lindström, U. ``Finding Space-Time Geometries without Using a Metric.'' Gen. Relativity Gravitation 15, 597-610, 1983.
- Parseval's Integral
- Parseval's Relation
- Parseval's Theorem
- Partial Derivative
- Partial Differential Equation
- Partial Fraction Decomposition
- Partial Latin Square
- Partially Ordered Set
- Partial Order
- Partial Quotient
- Particularly Well-Behaved Functions
- Partisan Game
- Partition
- Partition Function P
- Partition Function Q
- Part Metric
- Party Problem
- Parzen Apodization Function
- Pascal Distribution
- Pascal Line
- Pascal's Formula
- Pascal's Hexagrammum Mysticum
- Pascal's Limaçon
- Pascal's Rule
- Pascal's Theorem