AIMS Mathematics, 2017, 2(3): 545-556. doi: 10.3934/Math.2017.2.545.

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Applications of the lichnerowicz Laplacian to stress energy tensors

Department of Mathematics, University of Texas, TX 78539-2999 Edinburg, USA

A generalization of the Laplacian for p-forms to arbitrary tensors due to Lichnerowicz will be applied to a 2-tensor which has physical applications. It is natural to associate a divergencefree symmetric 2-tensor to a critical point of a specific variational problem and it is this 2-tensor that is studied. Numerous results are obtained for the stress-energy tensor, such as its divergence and Laplacian. A remarkable integral formula involving a symmetric 2-tensor and a conformal vector field is obtained as well.
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Keywords Basis; tensor; connection; differential system; Laplacian; bundle; harmonic map

Citation: Paul Bracken. Applications of the lichnerowicz Laplacian to stress energy tensors. AIMS Mathematics, 2017, 2(3): 545-556. doi: 10.3934/Math.2017.2.545


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