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

Research article

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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.
  Article Metrics


1. P. Baird, Stress-energy tensors and the Lichnerowicz Laplacian, J. of Geometry and Physics, 58(2008), 1329-1342.    

2. P. Blanchard and E. Brüning, Variational Methods in Mathematical Physics, Springer-Verlag, Berlin-Heidelberg, 1992.

3. S. S. Chern, Minimal surfaces in Euclidean Space of N dimensions: Symposium in Honor of Marston Morse, Princeton Univ. Press, 1965, 187-198.

4. J Eells and L. Lemaine, Selected Topics in Harmonic Maps: CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, 50 (1983).

5. A. Lichnerowicz, Géometrie des Groups de Transformations, Dunod, Paris, 1958.

6. A. Lichnerowicz, Propagateurs et commutateurs en relativité générale, Publ. Math. Inst. Hautes Ëtudes Sci., 10 (1961), 293-344.

7. P. Peterson, Riemannian Geometry, Springer-Verlag, NY, 1998.

8. R. Schoen, The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Comm. Pure and Applied Math. XLI, 317-392, 1988.

Copyright Info: © 2017, Paul Bracken, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved