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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.19739 |
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| _version_ | 1866912920564137984 |
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| author | Mikesh, Josef Stepanov, Sergey |
| author_facet | Mikesh, Josef Stepanov, Sergey |
| contents | This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize projective diffeomorphisms between Riemannian manifolds and one-parameter groups of projective diffeomorphisms (transformations) of a Riemannian manifold onto itself, respectively. This approach establishes a natural correspondence between analytical and geometric properties, enabling the study of projective diffeomorphisms via operator-theoretic methods. The proposed framework provides a new understanding of projective structures on Riemannian manifolds and extends classical results in differential geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Projective Maps from the Perspective of Elliptic Differential Operators Mikesh, Josef Stepanov, Sergey Differential Geometry 53C20, 35J15, 35J30 This paper develops an analytical approach to the study of the geometry of projective maps using the theory of elliptic differential operators. We construct two elliptic operators of second and fourth order, whose kernels characterize projective diffeomorphisms between Riemannian manifolds and one-parameter groups of projective diffeomorphisms (transformations) of a Riemannian manifold onto itself, respectively. This approach establishes a natural correspondence between analytical and geometric properties, enabling the study of projective diffeomorphisms via operator-theoretic methods. The proposed framework provides a new understanding of projective structures on Riemannian manifolds and extends classical results in differential geometry. |
| title | Projective Maps from the Perspective of Elliptic Differential Operators |
| topic | Differential Geometry 53C20, 35J15, 35J30 |
| url | https://arxiv.org/abs/2602.19739 |