The Ricci flow as a geodesic on the manifold of Riemannian metrics

Hajar Ghahremani-Gol | Asadollah Razavi

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=116890
Date :  2016/09/09
Publish in :    Journal of Contemporary Mathematical Analysis
DOI :  https://doi.org/10.3103/S1068362316050010
Link :  http://dx.doi.org/10.3103/S1068362316050010
Keywords :

Abstract :

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The Ricci flow is an evolution equation in the space of Riemannian metrics.A solution for this equation is a curve on the manifold of Riemannian metrics. In this paper we introduce a metric on the manifold of Riemannian metrics such that the Ricci flow becomes a geodesic.We show that the Ricci solitons introduce a special slice on the manifold of Riemannian metrics