On Perelman's Dilaton
| Autor: | Carlo Mantegazza, Zindine Djadli, Marco Maria Caldarelli, Giovanni Catino, Annibale Magni |
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| Přispěvatelé: | Marco, Caldarelli, Giovanni, Catino, Zindine, Djadli, Annibale, Magni, Mantegazza, Carlo Maria |
| Rok vydání: | 2008 |
| Předmět: |
Mathematics - Differential Geometry
010102 general mathematics Ricci flow Type (model theory) Space (mathematics) 01 natural sciences Action (physics) Gravitation General Relativity and Quantum Cosmology Mathematics - Analysis of PDEs Differential Geometry (math.DG) 0103 physical sciences Metric (mathematics) FOS: Mathematics Dilaton 010307 mathematical physics Geometry and Topology Diffeomorphism Mathematics::Differential Geometry 0101 mathematics Mathematics Mathematical physics Analysis of PDEs (math.AP) |
| Zdroj: | INSPIRE-HEP |
| DOI: | 10.48550/arxiv.0805.3268 |
| Popis: | By means of a Kaluza-Klein type argument we show that the Perelman's F-functional is the Einstein-Hilbert action in a space with extra ``phantom'' dimensions. In this way, we try to interpret some remarks of Perelman in the introduction and at the end of the first section in his first famous paper. As a consequence the Ricci flow (modified by a diffeomorphism and a time-dependent factor) is the evolution of the ``real'' part of the metric under a constrained gradient flow of the Einstein-Hilbert gravitational action in higher dimension. |
| Databáze: | OpenAIRE |
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