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Chapter 25: Lie Derivative, Invariance and Killing Vector Fields
https://doi.org/10.1142/9789813275386_0025Cited by:0 (Source: Crossref)
Abstract:
Let M be an n-dimensional C∞ differentiable manifold with local coordinates xj, j = 1, …, n. Real valued C∞ vector fields and real valued C∞ differential forms on M can be considered. The components of the vector field V are denoted by Vj∂/∂xj . This means
V := V1(x)∂∂x1 + V2(x)∂∂x2 + ⋯ + Vn(x)∂∂xn
in local coordinates. The Lie derivative of a differential form α with respect to V is defined by the derivative of α along the integral curve t ↦ Φt of V , i.e. LVα := limt→0 Φ*tα − α t.
