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Divergence theorems in semi-Riemannian geometry. (English) Zbl 0832.53050
From the author’s introduction: “In this paper, we will define a nondegenerate boundary of a semi-Riemannian manifold, and by making use of the volume form on the nondegenerate boundary, we will obtain two versions of the divergence theorem which are somewhat different from its usual form. And finally, we will state a version of the divergence theorem for two-dimensional Minkowski space”.

##### MSC:
 53C50 Lorentz manifolds, manifolds with indefinite metrics
##### Keywords:
nondegenerate boundary; volume form; divergence theorem
##### References:
 [1] Abraham, R., Marsden, J. E., and Ratiu, T.:Manifolds, Tensor Analysis and Applications, Addison-Wesley, Reading, Mass., 1983. [2] Bröcker, Th. and Jänich, K.:Introduction to Differential Topology, Cambridge University Press, Cambridge, 1982. [3] Duggal, K. L.: Affine conformal vector fields in semi-Riemannian manifolds,Acta Appl. Math. 23 (1991), 275–294. [4] O’Neill, B.:Semi-Riemannian Geometry, Academic Press, New York, 1983.