Next Article in Journal
Decision Support Framework for Digital Music Integration in Education Reform Using Picture Fuzzy FUCA and Industry–Academia Collaboration
Previous Article in Journal
Human–Robot Collaborative U-Shaped Disassembly Line Balancing Using Dynamic CRITIC–Entropy and Improved Honey Badger Optimization
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Symmetry
Volume 18
Issue 1
10.3390/sym18010146
symmetry-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Symmetric Tensors in Different Perspectives †

by
Anna Kimaczyńska
Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland
†
This paper is an extended version of our paper published in Kimaczyńska, A. The grad div operator. In Proceedings of the (Hyper) Complex Seminar 2023 in memoriam of Professor Julian Ławrynowicz, Online, 9–15 July 2023. Available online: https://www.youtube.com/watch?v=ZbG_YPw3i0k (accessed on 14 November 2025).
Symmetry 2026, 18(1), 146; https://doi.org/10.3390/sym18010146 (registering DOI)
Submission received: 21 November 2025 / Revised: 31 December 2025 / Accepted: 6 January 2026 / Published: 12 January 2026
(This article belongs to the Section Mathematics)
Versions Notes

Abstract

The main subject of this paper is the theme of differential operators defined for symmetric tensors on a Riemannian manifold and introduced in several new contexts. Some examples for 2-tensors are given and then the grad div operator for symmetric vector forms is defined. A few original operators in Rn related with grad div operator are discussed. Finally, important notions such as the Kenmotsu manifold, with some interesting examples, are also presented.
Keywords: commutator of an operator; divergence; gradient; grad div operator; Kenmotsu manifold; Riemannian manifold; symmetric derivative; symmetric tensor commutator of an operator; divergence; gradient; grad div operator; Kenmotsu manifold; Riemannian manifold; symmetric derivative; symmetric tensor

Share and Cite

MDPI and ACS Style

Kimaczyńska, A. Symmetric Tensors in Different Perspectives. Symmetry 2026, 18, 146. https://doi.org/10.3390/sym18010146

AMA Style

Kimaczyńska A. Symmetric Tensors in Different Perspectives. Symmetry. 2026; 18(1):146. https://doi.org/10.3390/sym18010146

Chicago/Turabian Style

Kimaczyńska, Anna. 2026. "Symmetric Tensors in Different Perspectives" Symmetry 18, no. 1: 146. https://doi.org/10.3390/sym18010146

APA Style

Kimaczyńska, A. (2026). Symmetric Tensors in Different Perspectives. Symmetry, 18(1), 146. https://doi.org/10.3390/sym18010146

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop