Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
In this work, we study actions of the Lie group SL(2,C) on a complex manifold of dimension three or higher. It is demonstrated that these types of actions induce three complete holomorphic vector fields, one of which is periodic, and that there exists a particular relationship between them, given b...
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| Main Author: | |
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| Format: | Article |
| Language: | Spanish |
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Universidad Nacional de Trujillo
2024-12-01
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| Series: | Selecciones Matemáticas |
| Subjects: | |
| Online Access: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6159 |
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| Summary: | In this work, we study actions of the Lie group SL(2,C) on a complex manifold of dimension three or higher.
It is demonstrated that these types of actions induce three complete holomorphic vector fields, one of which is periodic, and that there exists a particular relationship between them, given by the Lie bracket, which generates a singular holomorphic foliation of codimension two. Subsequently, the types of singularities are classified, and the normal forms of these vector fields are obtained in a neighborhood of each singular point of the foliation. |
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| ISSN: | 2411-1783 |