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arXiv · 0805.3268

On Perelman's Dilaton

Marco Caldarelli·Giovanni Catino·Zindine Djadli·Annibale Magni·Carlo Mantegazza
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Abstract

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.

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Marco Caldarelli, Giovanni Catino, Zindine Djadli, Annibale Magni, Carlo Mantegazza. 2008-05-21. On Perelman's Dilaton. https://doi.org/10.1007/s10711-009-9410-1

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