Harmonic Gauge on the Space of Riemannian Metrics and Its Role in the Ricci-DeTurck Flow
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911635993526272 |
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| author | Sergey, Stepanov |
| author_facet | Sergey, Stepanov |
| contents | We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates divergence-type terms in the first variation of the Hilbert-Einstein functional and induces a natural elliptic structure for the second variation. As a consequence, positivity of the curvature operator of the second kind implies spectral stability of the functional. This establishes a conceptual link between gauge fixing, elliptic operator theory, and geometric rigidity, and provides a variational counterpart to the Ricci-DeTurck mechanism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_27663 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Harmonic Gauge on the Space of Riemannian Metrics and Its Role in the Ricci-DeTurck Flow Sergey, Stepanov Differential Geometry 53C20, 53C21, 53C44, 53C25 We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates divergence-type terms in the first variation of the Hilbert-Einstein functional and induces a natural elliptic structure for the second variation. As a consequence, positivity of the curvature operator of the second kind implies spectral stability of the functional. This establishes a conceptual link between gauge fixing, elliptic operator theory, and geometric rigidity, and provides a variational counterpart to the Ricci-DeTurck mechanism. |
| title | Harmonic Gauge on the Space of Riemannian Metrics and Its Role in the Ricci-DeTurck Flow |
| topic | Differential Geometry 53C20, 53C21, 53C44, 53C25 |
| url | https://arxiv.org/abs/2604.27663 |