Killing vector fields

Calculus on Manifolds

Published in Mattias Blennow, Mathematical Methods for Physics and Engineering, 2018

for all other vector fields Y and Z. Show that the Killing vector field satisfies () ∇aXb+∇bXa=0in any coordinate system and that this is also a sufficient condition for the vector field X to be a Killing vector field.Show that the Lie bracket of any two Killing vector fields is also a Killing vector field.For any geodesic γ with an affine parameter t, show that () Q=g(X, γ˙),where γ˙ is the tangent vector of γ, is constant along the geodesic.

Estimates for the volume variation of compact submanifolds driven by a stochastic flow

View Article

Journal Information

Published in Dynamical Systems, 2022

Diego Sebastian Ledesma, Robert Andres Galeano Anaya, Fabiano Borges da Silva

Finally, we present below the conditions that we make for most of this work: The vectors fields are smooth (), satisfy and we have the solution flow associated with the SDE (1) for . is a Killing vector field for h, that is, we have that the Lie derivative of h with respect to this vector field is zero: The vectors fields satisfy for all bilinear form .

Killing vector fields

Explore chapters and articles related to this topic

Calculus on Manifolds

Estimates for the volume variation of compact submanifolds driven by a stochastic flow