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JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, vol.16, no.2, pp.161-168, 2009 (SCI-Expanded)
In this paper, we study the geodesic completeness of nondegenerate submanifolds in semi-Euclidean spaces by extending the study of Beem and Ehrlich [ 1] to semi-Euclidean spaces. From the physical point of view, this extend may have a significance that a semi-Euclidean space contains more variety of Lorentzian submanifolds rather than those of Lorentzian hypersurfaces in a Minkowski space as in [ 1]. From mathematical point of view, since there is no distinction in the analysis of geodesic completeness of Lorentzian submanifolds and nondegenerate submanifolds in a semi-Euclidean space, we treat the mathematically more general case of nondegenerate submanifolds in a semi-Euclidean space. The new ideas leading to this generalization are the sufficient conditions for algorithms in the proofs of the results in [ 1]. Indeed these sufficient conditions for the algorithms also work well for the nondegenerate submanifolds in a semi-Euclidean space.