A visual introduction to curved geometry for physicists
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908913356505088 |
|---|---|
| author | Urbański, Karol |
| author_facet | Urbański, Karol |
| contents | This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build intuition for all types of Riemannian and Lorentzian manifolds of constant curvature. A visual derivation of the Thomas precession is given, showcasing the utility of differential geometry while also pointing a spotlight at certain intricacies of Minkowski space crucial from a pedagogical perspective. In addition, a straightforward method to generate some Carter-Penrose diagrams -- suitable for students with no differential geometry knowledge -- is presented, and a new method of indicating distortion on spacetime diagrams is shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24409 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A visual introduction to curved geometry for physicists Urbański, Karol Physics Education General Relativity and Quantum Cosmology This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build intuition for all types of Riemannian and Lorentzian manifolds of constant curvature. A visual derivation of the Thomas precession is given, showcasing the utility of differential geometry while also pointing a spotlight at certain intricacies of Minkowski space crucial from a pedagogical perspective. In addition, a straightforward method to generate some Carter-Penrose diagrams -- suitable for students with no differential geometry knowledge -- is presented, and a new method of indicating distortion on spacetime diagrams is shown. |
| title | A visual introduction to curved geometry for physicists |
| topic | Physics Education General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.24409 |