Divergence of multivector fields on infinite-dimensional manifolds

Abstract

UDC 514.763.2+515.164.17 We study the divergence of multivector fields on Banach manifolds with a Radon measure. We propose an infinite-dimensional version of divergence consistent with the classical divergence from finite-dimensional differential geometry. We then transfer certain natural properties of the divergence operator to the infinite-dimensional setting. Finally, we study the relation between the divergence operator on a manifold M and the divergence operator on a submanifold S ⊂ M .