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**Nota de Física****Publicado**

# **Surfaces of Constant Negative Scalar Curvature and the Correpondence Between the Liouville and the Sine-Gordon, Equations**

**H. Belich Jr; G. Cuba; R. Paunov**

1999

[**Descargar PDF **0,2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb465/pdf) [**Contactar al responsable**](mailto:apub@cbpf.br?subject=Surfaces%20of%20Constant%20Negative%20Scalar%20Curvature%20and%20the%20Correpondence%20Between%20the%20Liouville%20and%20the%20Sine-Gordon%2C%20Equations)

## **Datos de la publicación**

<dl>

<dt>Autores</dt>
<dd>H. Belich Jr; G. Cuba; R. Paunov</dd>

<dt>Tipo</dt>
<dd>Nota de Física</dd>

<dt>Estado</dt>
<dd>Publicado</dd>

<dt>Fecha de publicación</dt>
<dd>1999</dd>

<dt>Descripción</dt>
<dd>By studying the it ''internal'' Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville and the sine-Gordon equations. First, considering isometric immersions into the Lobachevskian plane, we obtain an uniform expression for the general (locally defined) solution of both the equations. Second, we prove that there is a Lie-Bäcklund transformation interpolating between Liouville and sine-Gordon. Third, we use isometric immersions into the Lobachevskian plane to describe sine-Gordon N-solitons explicitely.</dd>

<dt>Año</dt>
<dd>1999</dd>

<dt>Número</dt>
<dd>CBPF-NF-044/99</dd>

<dt>Vínculo con tesis</dt>
<dd>No</dd>

<dt>Vínculo con beca</dt>
<dd>No</dd>

</dl>

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```

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