## Abstract

The Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on the boundary. This facts explain why we could not find the solution of the system on the boundary in terms of known functions. We make the stability analysis of the helicoid and catenoid cases and end up with an Appendix which gives a new example wherein one encounters a form of the Heun equation.

Original language | English |
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Article number | 054101 |

Journal | Journal of Mathematical Physics |

Volume | 49 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 May 2008 |

### Funding

We would like to thank Professor Ayşe Bilge for correspondence and discussions. This work is supported by TÜBİTAK, which is The Scientific and Technological Council of Turkey. The work of M.H. is also supported by TÜBA, which is the Academy of Sciences of Turkey.

Funders | Funder number |
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Academy of Sciences of Turkey | |

TÜBİTAK | |

Türkiye Bilimsel ve Teknolojik Araştirma Kurumu |