Divergence of multivector fields on infinite-dimensional manifolds

  • Yu. Bogdanskii Nat. Techn. Univ. Ukraine ``Igor Sikorsky Kyiv Polytechnic Institute’’
  • V. Shram Univ. Bonn, Germany
Keywords: Banach manifold, Radon measure, multivector field, divergence, surface measure

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 ${\rm div}_M$ on a manifold $M$ and the divergence operator ${\rm div}_S$ on a submanifold  $S \subset M.$

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Published
17.01.2023
How to Cite
BogdanskiiY., and ShramV. “Divergence of Multivector Fields on Infinite-Dimensional Manifolds”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 12, Jan. 2023, pp. 1640 -53, doi:10.37863/umzh.v74i12.6522.
Section
Research articles