Roque, Waldir L.; Dos Santos, Renato P. Computer algebra in spacetime embedding. (English) Zbl 0748.53001 J. Symb. Comput. 12, No. 3, 381-389 (1991). Let \(V^ 4\) be a spacetime (= a pseudo-Riemannian manifold of signature (3,1)), isometrically embedded in a pseudo-Euclidean manifold \(M^{4+n}\). The main result of the paper is an algorithm, which determines the normal vectors to \(V^ 4\) in \(M^{4+n}\) and then finds the second fundamental form and the torsion vector. The authors mention, that they implemented the algorithm in the algebraic computing system REDUCE. As an example they study the Schwarzschild spacetime, embedded in a 6-dimensional pseudo-Euclidean manifold. Reviewer: C.Bär (Bonn) Cited in 1 Document MSC: 53-04 Software, source code, etc. for problems pertaining to differential geometry 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 68W30 Symbolic computation and algebraic computation Keywords:Schwarzschild solution; second fundamental form; algorithm; normal vectors; torsion vectors Software:REDUCE PDFBibTeX XMLCite \textit{W. L. Roque} and \textit{R. P. Dos Santos}, J. Symb. Comput. 12, No. 3, 381--389 (1991; Zbl 0748.53001) Full Text: DOI arXiv References: [1] Davenport, J. H.; Siret, Y.; Tournier, E., (Computer Algebra: Systems and Algorithms for Algebraic Computation (1988), Academic Press) · Zbl 0679.68058 [2] Eisenhart, L. P., (Riemannian Geometry (1946), Princeton University Press) [3] Hawking, S. W.; Ellis, G. F.R., (The Large Scale Structure of Space-Time (1973), Cambridge University Press) · Zbl 0265.53054 [4] Hearn, A. C., (REDUCE Manual (1986), The Rand Corporation: The Rand Corporation Santa Monica) [5] Maia, M. D., The Physics of the Gauss-Codazzi-Ricci Equations, Mat. Aplic. Comp.. (On Kaluza-Klein Relativity. On Kaluza-Klein Relativity, Gen. Rel. Grav., 18 (1986)), 5, 695-699 (1986) · Zbl 0648.53044 [6] Maia, M. D.; Roque, W. L., Classical Membrane Cosmology, Phys. Lett. A, 139, 121-124 (1988) [7] Rayna, G., (REDUCE; A Software for Algebraic Computation (1987), Springer-Verlag) · Zbl 0642.68060 [8] Rosen, J., Embedding of Various Relativistic Riemannian Spaces in Pseudo-Euclidean Spaces, Rev. Mod. Phys, 87, 204-214 (1965) · Zbl 0125.21203 [9] Stauffer, D.; Hehl, F. W.; Winkelmann, V.; Zabolitsky, J. G., (Computer Simulation and Computer Algebra (1988), Springer-Verlag) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.