Geometric Interpretations and Applications of the Berger-Ebin and York $L^2$-Orthogonal Decompositions
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| Format: | Preprint |
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2025
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| _version_ | 1866913855190335488 |
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| author | Stepanov, Sergey Tsyganok, Irina |
| author_facet | Stepanov, Sergey Tsyganok, Irina |
| contents | The Berger-Ebin and York $L^2$-orthogonal decompositions of the vector space of symmetric bilinear differential two-forms are fundamental tools in global Riemannian geometry. In this paper, we investigate the structure of Ricci tensors on compact Riemannian manifolds, with a particular focus on compact Ricci almost solitons, utilizing both the Berger-Ebin and York $L^2$-orthogonal decompositions. In addition, we explore applications of the York $L^2$-orthogonal decomposition to the theory of submanifolds and to the study of harmonic maps between Riemannian manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_17566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Interpretations and Applications of the Berger-Ebin and York $L^2$-Orthogonal Decompositions Stepanov, Sergey Tsyganok, Irina Differential Geometry 53C20, 53C21, 53C24, 53A10 The Berger-Ebin and York $L^2$-orthogonal decompositions of the vector space of symmetric bilinear differential two-forms are fundamental tools in global Riemannian geometry. In this paper, we investigate the structure of Ricci tensors on compact Riemannian manifolds, with a particular focus on compact Ricci almost solitons, utilizing both the Berger-Ebin and York $L^2$-orthogonal decompositions. In addition, we explore applications of the York $L^2$-orthogonal decomposition to the theory of submanifolds and to the study of harmonic maps between Riemannian manifolds. |
| title | Geometric Interpretations and Applications of the Berger-Ebin and York $L^2$-Orthogonal Decompositions |
| topic | Differential Geometry 53C20, 53C21, 53C24, 53A10 |
| url | https://arxiv.org/abs/2505.17566 |