On the Generalized Projective Riemann Curvature in Finsler Geometry
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911282814255104 |
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| author | Sadeghzadeh, Nasrin Yaghoubi, Masoumeh |
| author_facet | Sadeghzadeh, Nasrin Yaghoubi, Masoumeh |
| contents | This paper explores the generalized projective Riemann curvature in Finsler geometry, focusing on the properties of projectively equivalent Finsler metrics and the invariance of their curvature structures under projective transformations. We extend the existing frameworks of projective Riemann and Ricci curvatures by introducing new characterizations of quadratic curvature properties, highlighting their geometric significance in the broader context of Finsler manifolds. Our results provide novel insights into curvature behavior under generalized projective sprays and contribute to a deeper understanding of intrinsic geometric invariants within projective classes of Finsler spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Generalized Projective Riemann Curvature in Finsler Geometry Sadeghzadeh, Nasrin Yaghoubi, Masoumeh Differential Geometry 53B40, 53C60 This paper explores the generalized projective Riemann curvature in Finsler geometry, focusing on the properties of projectively equivalent Finsler metrics and the invariance of their curvature structures under projective transformations. We extend the existing frameworks of projective Riemann and Ricci curvatures by introducing new characterizations of quadratic curvature properties, highlighting their geometric significance in the broader context of Finsler manifolds. Our results provide novel insights into curvature behavior under generalized projective sprays and contribute to a deeper understanding of intrinsic geometric invariants within projective classes of Finsler spaces. |
| title | On the Generalized Projective Riemann Curvature in Finsler Geometry |
| topic | Differential Geometry 53B40, 53C60 |
| url | https://arxiv.org/abs/2511.18289 |