Divergence of multivector fields on infinite-dimensional manifolds
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.&a...
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| Date: | 2023 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6522 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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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| DOI: | 10.37863/umzh.v74i12.6522 |