Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary
Ezin, Jean-Pierre ; Hassirou, Mouhamadou ; Tossa, Joel
Kodai Math. J., Tome 30 (2007) no. 1, p. 41-54 / Harvested from Project Euclid
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We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. We obtain a generalization of results obtained by Ünal in [9, Acta Appl. Math. 40(1995)] and E. García-Río and D. N. Kupeli in [4, Proceeding of the Third World Congress of Nonlinear Analysts, Part 5 (Catania, 2000). Nonlinear Anal. 47 (5) 2995-3004, 2001]. ¶ As a tool, we use an induced volume form on the degenerate boundary by introducing a star like operator. ¶ A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained.
Publié le : 2007-03-14
Classification:  
@article{1175287620,
     author = {Ezin, Jean-Pierre and Hassirou, Mouhamadou and Tossa, Joel},
     title = {Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary},
     journal = {Kodai Math. J.},
     volume = {30},
     number = {1},
     year = {2007},
     pages = { 41-54},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175287620}
}

Ezin, Jean-Pierre; Hassirou, Mouhamadou; Tossa, Joel. Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary. Kodai Math. J., Tome 30 (2007) no. 1, pp.  41-54. http://gdmltest.u-ga.fr/item/1175287620/