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Divergence of Multivector Fields on Infinite-Dimensional Manifolds

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Ukrainian Mathematical Journal Aims and scope

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

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Author notes

  1. Yu. Bogdanskii is deceased.

Authors and Affiliations

  1. “I. Sikorsky Kyiv Polytechnic Institute”, National Technical University of Ukraine, Kyiv, Ukraine

    Yu. Bogdanskii

  2. Universität Bonn, Bonn, Germany

    V. Shram

Authors
  1. Yu. Bogdanskii
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  2. V. Shram
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Corresponding author

Correspondence to V. Shram.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 12, pp. 1640–1653, December, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i12.6522.

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Bogdanskii, Y., Shram, V. Divergence of Multivector Fields on Infinite-Dimensional Manifolds. Ukr Math J 74, 1872–1887 (2023). https://doi.org/10.1007/s11253-023-02175-w

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  • DOI: https://doi.org/10.1007/s11253-023-02175-w

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