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The Weitzenböck formula for the divgrad operator

Volume 130 / 2023

Anna Kimaczyńska Annales Polonici Mathematici 130 (2023), 223-252 MSC: Primary 53C15; Secondary 47F05, 53C21. DOI: 10.4064/ap220801-13-2 Published online: 26 July 2023

Abstract

The paper concerns symmetric tensors and consists of interesting formulas having also consequences in geometry. First, the differential operators of gradient and of divergence in the bundles of symmetric tensors and symmetric tensors with values in the tangent bundle, respectively, are investigated, leading to a new, simple proof of the Weitzenböck formula. In the second part of this paper the differential operators and symmetric forms on $\mathbb R^n$ are investigated as an application of previous considerations.

Authors

  • Anna KimaczyńskaFaculty of Mathematics and Computer Science
    University of Łódź
    90-238 Łódź, Poland
    e-mail

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