Research output: Contribution to journal › Conference article › peer-review
Explicit isometric embeddings of pseudo-Riemannian manifolds : Ideas and applications. / Sheykin, A. A.; Markov, M. V.; Fedulov, Ya A.; Paston, S. A.
In: Journal of Physics: Conference Series, Vol. 1697, No. 1, 012077, 17.12.2020.Research output: Contribution to journal › Conference article › peer-review
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TY - JOUR
T1 - Explicit isometric embeddings of pseudo-Riemannian manifolds
T2 - International Conference PhysicA.SPb 2020
AU - Sheykin, A. A.
AU - Markov, M. V.
AU - Fedulov, Ya A.
AU - Paston, S. A.
N1 - Funding Information: The work of A. S. and S. P. is supported by RFBR Grant No. 20-01-00081. The authors are grateful to D. P. Solovyev for the useful references and to A. N. Starodubtsev for valuable discussions. Publisher Copyright: © Published under licence by IOP Publishing Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/12/17
Y1 - 2020/12/17
N2 - We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method, which is based on the idea that the exterior symmetry of the embedded surface and the interior symmetry of its metric must be the same. In case of high enough symmetry of the metric such method allows transforming the expression for induced metric, which is the one to be solved in order to construct an embedding, into a system of ODEs. It turns out that this method can be generalized to allow the surface to have lower symmetry as long as the above simplification occurs. This generalization can be used in the construction of embeddings for metrics, whose symmetry group is hard to analyze, and the construction of the isometrically deformed (bent) surface. We give some examples of the application of this method. In particular, we construct the embedding of spatially-flat Friedmann model and isometric bendings of a sphere, 3-sphere, and squashed AdS universe, which is related to the Godel universe.
AB - We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method, which is based on the idea that the exterior symmetry of the embedded surface and the interior symmetry of its metric must be the same. In case of high enough symmetry of the metric such method allows transforming the expression for induced metric, which is the one to be solved in order to construct an embedding, into a system of ODEs. It turns out that this method can be generalized to allow the surface to have lower symmetry as long as the above simplification occurs. This generalization can be used in the construction of embeddings for metrics, whose symmetry group is hard to analyze, and the construction of the isometrically deformed (bent) surface. We give some examples of the application of this method. In particular, we construct the embedding of spatially-flat Friedmann model and isometric bendings of a sphere, 3-sphere, and squashed AdS universe, which is related to the Godel universe.
UR - http://www.scopus.com/inward/record.url?scp=85098325133&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/1697/1/012077
DO - 10.1088/1742-6596/1697/1/012077
M3 - Conference article
AN - SCOPUS:85098325133
VL - 1697
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012077
Y2 - 19 October 2020 through 23 October 2020
ER -
ID: 72597052