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A New Strong Laplacian on Differential Forms

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Abstract

We construct a strong Laplacian D * D by using the third operator in the basis {d,d *,D} of the space of natural first-order operators acting on the differential forms of a Riemannian manifold (M,g). We study the properties of the Laplacian D * D and obtain Weitzenbock's formula relating the three strong Laplacians dd *, d * d, and D * D to the curvature of the manifold (M,g).

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  1. Vladimir State Pedagogical University, russia

    S. E. Stepanov

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  1. S. E. Stepanov
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Stepanov, S.E. A New Strong Laplacian on Differential Forms. Mathematical Notes 76, 420–425 (2004). https://doi.org/10.1023/B:MATN.0000043469.63097.c9

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  • DOI: https://doi.org/10.1023/B:MATN.0000043469.63097.c9

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