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Computer algebra in spacetime embedding. (English) Zbl 0748.53001

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)

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

Software:

REDUCE
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References:

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