1
$\begingroup$

An interesting class of contact manifolds is the class of $K$-contact manifolds ($\mathcal{L}_\xi g=0$) which have been studied by many authors. It is natural to study conformal Killing-contact manifolds. This means that the characteristic vector field satisfies the conformal killing equation; i. e. $\mathcal{L}_\xi g=\sigma g$ where $\sigma$ is a smooth function on $M$. Why is this structure not studied?

$\endgroup$

1 Answer 1

1
$\begingroup$

The reason is that the g-trace of the conformal Killing equation gives 2(divergence of characteristic vector field)=n(sigma). But divergence of characteristic vector field on a contact metric manifold is zero. Hence, sigma = 0. Thus it reduces to the K-contact manifold.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.