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It is often easier to study pseudo-Riemannian manifolds by presenting them assurfaces in some ambient space. We propose an algorithm for construction ofexplicit isometric embeddings of pseudo-Riemannian manifolds with symmetriesinto an ambient space of higher dimension. While most of the existing methodsare based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use them andinstead concentrate on a system of equations which connects the metric on themanifold and the embedding function of the surface. Our algorithm is based onthe group theoretical method of separation of variables that we developedearlier (arXiv:1202.1204). The algorithm makes this method more convenient andsimple to use. It allowed us to simplify the construction of many knownembeddings as well as obtain some new ones. In particular, we obtain explicitglobal embeddings of spinning BTZ black hole in 7-dimensional flat space.

Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction