Duality and Some Links Between Riemannian Submersion, F-Harmonicity, and Cohomology

Fundamentally, duality gives two different points of view of looking at the same object. It appears in many subjects in mathematics (geometry, algebra, analysis, PDEs, Geometric Measure Theory, etc.) and in physics. For example, Connections on Fiber Bundles in mathematics, and Gauge Fields in physic...

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Bibliographic Details
Published inAxioms Vol. 14; no. 3; p. 162
Main Authors Chen, Bang-Yen, Wei, Shihshu (Walter)
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 23.02.2025
Subjects
Algebra
Analysis
cohomology class
duality
F-harmonic maps
Homology
Mathematics
minimal submanifold
Neighborhoods
p-harmonic morphism
Physics
Riemannian submersion
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United States
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Summary:Fundamentally, duality gives two different points of view of looking at the same object. It appears in many subjects in mathematics (geometry, algebra, analysis, PDEs, Geometric Measure Theory, etc.) and in physics. For example, Connections on Fiber Bundles in mathematics, and Gauge Fields in physics are exactly the same. In n-dimensional geometry, a fundamental notion is the “duality” between chains and cochains, or domains of integration and the integrands. In this paper, we extend ideas given in our earlier articles and connect seemingly unrelated areas of F-harmonic maps, f-harmonic maps, and cohomology classes via duality. By studying cohomology classes that are related with p-harmonic morphisms, F-harmonic maps, and f-harmonic maps, we extend several of our previous results on Riemannian submersions and p-harmonic morphisms to F-harmonic maps and f-harmonic maps, which are Riemannian submersions.
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14030162