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Notes on Harmonic Tensor Fields

In: New Developments in Differential Geometry, Budapest 1996

Author

Listed:
  • E. García-Río

    (Universidade de Santiago de Compostela, Departamento de Análise Matemática Facultade de Matemáticas)

  • L. Vanhecke

    (Katholieke Universiteit Leuven, Department of Mathematics)

  • M. E. Vázquez-Abal

    (Universidade de Santiago de Compostela, Departamento de Xeometría e Topoloxía Facultade de Matemáticas)

Abstract

We review some basic facts and examples of harmonic (1,1)- and (1,2)-tensor fields. This leads to the consideration of vector fields defining harmonic sections of the tangent bundle. Finally, by the study of the musical isomorphisms, a correspondence is obtained between vector fields and one-forms defining harmonic sections of the tangent and the cotangent bundle, respectively.

Suggested Citation

  • E. García-Río & L. Vanhecke & M. E. Vázquez-Abal, 1999. "Notes on Harmonic Tensor Fields," Springer Books, in: J. Szenthe (ed.), New Developments in Differential Geometry, Budapest 1996, pages 123-142, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5276-1_8
    DOI: 10.1007/978-94-011-5276-1_8
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