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The exterior derivative as a Killing vector field

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Abstract

Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.

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Authors and Affiliations

  1. Dept. de Geometria i Topologia, Facultat de Matemàtiques, Universitat de València, C/Dr. Moliner 50, 46100, Burjassot (València), Spain

    J. Monterde

  2. Centro de Investigación en Matemáticas, Apdo. Postal, 402, C.P. 36000, Guanajuato, Gto., México

    O. A. Sánchez-Valenzuela

Authors
  1. J. Monterde
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  2. O. A. Sánchez-Valenzuela
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Corresponding author

Correspondence to J. Monterde.

Additional information

Partially supported by DGICYT grants #PB91-0324, and SAB94-0311; CONACyT grant #3189-E9307.

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Monterde, J., Sánchez-Valenzuela, O.A. The exterior derivative as a Killing vector field. Israel J. Math. 93, 157–170 (1996). https://doi.org/10.1007/BF02761099

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  • DOI: https://doi.org/10.1007/BF02761099

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