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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.03353 |
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| _version_ | 1866929578773053440 |
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| author | Choudhury, Shouvik Datta |
| author_facet | Choudhury, Shouvik Datta |
| contents | In this paper, we investigate the evolution of certain functionals involving higher powers of a scalar quantity $F$ under Bernard List's extended Ricci flow on a compact Riemannian manifold. By deriving explicit expressions for the time derivative of integrals of the form $\int_M F^n \cdot \frac{\partial F}{\partial t} \, dμ$ for various powers $n$, we explore the intricate interplay between geometric quantities and scalar functions without making any assumptions about the manifold, the scalar field $Φ$, or the function $u$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Evolution of Functionals Under Extended Ricci Flow Choudhury, Shouvik Datta Differential Geometry In this paper, we investigate the evolution of certain functionals involving higher powers of a scalar quantity $F$ under Bernard List's extended Ricci flow on a compact Riemannian manifold. By deriving explicit expressions for the time derivative of integrals of the form $\int_M F^n \cdot \frac{\partial F}{\partial t} \, dμ$ for various powers $n$, we explore the intricate interplay between geometric quantities and scalar functions without making any assumptions about the manifold, the scalar field $Φ$, or the function $u$. |
| title | Evolution of Functionals Under Extended Ricci Flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.03353 |