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Mathematics > Differential Geometry

arXiv:0710.3342 (math)
[Submitted on 17 Oct 2007 (v1), last revised 14 Jul 2009 (this version, v4)]

Title:The Conjugate Linearized Ricci Flow on Closed 3-Manifolds

Authors:Mauro Carfora
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Abstract: We characterize the conjugate linearized Ricci flow and the associated backward heat kernel on closed three--manifolds of bounded geometry. We discuss their properties, and introduce the notion of Ricci flow conjugated constraint sets which characterizes a way of Ricci flow averaging metric dependent geometrical data. We also provide an integral representation of the Ricci flow metric itself and of its Ricci tensor in terms of the heat kernel of the conjugate linearized Ricci flow. These results, which readily extend to closed n-dimensional manifolds, yield for various conservation laws, monotonicity and asymptotic formulas for the Ricci flow and its linearization.
Comments: We added a few references and indications of which result extends to n-dimensional manifold. A few complex computations have been presented in full detail. This version of the paper matches the work to appear in Annali della Scuola Normale Superiore di Pisa
Subjects: Differential Geometry (math.DG); Mathematical Physics (math-ph)
MSC classes: 53C44, 53C21
Cite as: arXiv:0710.3342 [math.DG]
  (or arXiv:0710.3342v4 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.3342

Submission history

From: Mauro Carfora [view email]
[v1] Wed, 17 Oct 2007 16:19:57 UTC (49 KB)
[v2] Thu, 3 Apr 2008 13:51:29 UTC (57 KB)
[v3] Wed, 3 Jun 2009 09:21:32 UTC (60 KB)
[v4] Tue, 14 Jul 2009 09:07:18 UTC (60 KB)
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