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 -