# Two-dimensional imaginary lobachevsky space. Separation of variables and contractions

## Abstract

The Inoenue-Wigner contraction from the SO(2, 1) group to the E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the corresponding two-dimensional homogeneous spaces: two-dimensional one sheeted hyperboloid and two-dimensional pseudo-Euclidean space. Here we consider the contraction limits of some basis functions for the subgroup coordinates only.

- Authors:

- Universidad de Guadalajara, Departamento de Matematicas, CUCEI (Mexico)

- Publication Date:

- OSTI Identifier:
- 22043884

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Atomic Nuclei

- Additional Journal Information:
- Journal Volume: 74; Journal Issue: 7; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COORDINATES; EUCLIDEAN SPACE; LOBACHEVSKY GEOMETRY; SO GROUPS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Pogosyan, G. S., E-mail: pogosyan@theor.jinr.ru, and Yakhno, A.
```*Two-dimensional imaginary lobachevsky space. Separation of variables and contractions*. United States: N. p., 2011.
Web. doi:10.1134/S106377881106024X.

```
Pogosyan, G. S., E-mail: pogosyan@theor.jinr.ru, & Yakhno, A.
```*Two-dimensional imaginary lobachevsky space. Separation of variables and contractions*. United States. doi:10.1134/S106377881106024X.

```
Pogosyan, G. S., E-mail: pogosyan@theor.jinr.ru, and Yakhno, A. Fri .
"Two-dimensional imaginary lobachevsky space. Separation of variables and contractions". United States. doi:10.1134/S106377881106024X.
```

```
@article{osti_22043884,
```

title = {Two-dimensional imaginary lobachevsky space. Separation of variables and contractions},

author = {Pogosyan, G. S., E-mail: pogosyan@theor.jinr.ru and Yakhno, A.},

abstractNote = {The Inoenue-Wigner contraction from the SO(2, 1) group to the E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the corresponding two-dimensional homogeneous spaces: two-dimensional one sheeted hyperboloid and two-dimensional pseudo-Euclidean space. Here we consider the contraction limits of some basis functions for the subgroup coordinates only.},

doi = {10.1134/S106377881106024X},

journal = {Physics of Atomic Nuclei},

issn = {1063-7788},

number = 7,

volume = 74,

place = {United States},

year = {2011},

month = {7}

}

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