Öz The Cayley transform maps the unit disk onto the upper half-plane, conformally and isometrically. In this paper, we generalize the Cayley transform in three-dimensional homogeneous geometries which are fiber bundles over the hyperbolic plane. Obtained generalizations are isometries between existing models in corresponding homogeneous geometries. Particularly, constructed isometry between two models of { $\widetilde{SL(2,\mathbb{R})}$} geometry is nontrivial and enables comparison and transfer of known and even future results between these two models.

Anahtar Kelimeler:
##
Cayley transform,
homogeneous geometry,
isometry

Bibtex | `@ { tbtkmath575205, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {}, publisher = {TÜBİTAK}, year = {2018}, volume = {42}, pages = {2942 - 2952}, doi = {}, title = {Generalization of the Cayley transform in 3D homogeneous geometries}, key = {cite}, author = {Erjavec, ZLATKO} }` |

APA | Erjavec, Z . (2018). Generalization of the Cayley transform in 3D homogeneous geometries . Turkish Journal of Mathematics , 42 (6) , 2942-2952 . |

MLA | Erjavec, Z . "Generalization of the Cayley transform in 3D homogeneous geometries" . Turkish Journal of Mathematics 42 (2018 ): 2942-2952 < |

Chicago | Erjavec, Z . "Generalization of the Cayley transform in 3D homogeneous geometries". Turkish Journal of Mathematics 42 (2018 ): 2942-2952 |

RIS | TY - JOUR T1 - Generalization of the Cayley transform in 3D homogeneous geometries AU - ZLATKO Erjavec Y1 - 2018 PY - 2018 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 2942 EP - 2952 VL - 42 IS - 6 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2021 ER - |

EndNote | %0 Turkish Journal of Mathematics Generalization of the Cayley transform in 3D homogeneous geometries %A ZLATKO Erjavec %T Generalization of the Cayley transform in 3D homogeneous geometries %D 2018 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 42 %N 6 %R %U |

ISNAD | Erjavec, ZLATKO . "Generalization of the Cayley transform in 3D homogeneous geometries". Turkish Journal of Mathematics 42 / 6 (Aralık 2018): 2942-2952 . |

AMA | Erjavec Z . Generalization of the Cayley transform in 3D homogeneous geometries. Turkish Journal of Mathematics. 2018; 42(6): 2942-2952. |

Vancouver | Erjavec Z . Generalization of the Cayley transform in 3D homogeneous geometries. Turkish Journal of Mathematics. 2018; 42(6): 2942-2952. |

IEEE | Z. Erjavec , "Generalization of the Cayley transform in 3D homogeneous geometries", Turkish Journal of Mathematics, c. 42, sayı. 6, ss. 2942-2952, Ara. 2018 |

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