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On Perelman's Dilaton
- Source :
- Geom Dedicata (2010) 145:127-137
- Publication Year :
- 2008
-
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.
- Subjects :
- Mathematics - Differential Geometry
Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Journal :
- Geom Dedicata (2010) 145:127-137
- Publication Type :
- Report
- Accession number :
- edsarx.0805.3268
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10711-009-9410-1