On deformation of Riemannian metrics quadratic in the Ricci tensor
type: Item
instance of: scholarly article
title: On deformation of Riemannian metrics quadratic in the Ricci tensor
zbMATH Open document ID: 1261.53066
DOI: 10.1134/S0037446612020309
author: A. N. Plotnikova
published in: Siberian Mathematical Journal
publication date: 2012-11-14T00:00:00Z
review text: The author proves the short-time existence of solution of the following quadratic flow \[ \frac{\partial g_{ij}}{\partial t}=-2R_{ij}+\lambda (x)R_i^lR_{lj} \] on compact manifold \(M\) when the function \(\lambda\in C^{\infty}(M)\) is sufficiently small in \(L^{\infty}\) norm. They also construct formulas of the deformation of the Ricci tensor for this flow.
reviewed by: Shu-Yu Hsu
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 6105699
zbMATH Keywords: Riemannian metric
zbMATH Keywords: Ricci curvature
zbMATH Keywords: De Turk trick
zbMATH Keywords: linearization
Wikidata QID: Q115248562
MaRDI profile type: Publication
cites work: Three-manifolds with positive Ricci curvature
cites work: Q5485637
cites work: Q5485638
cites work: Deforming the metric on complete Riemannian manifolds
description: scientific article; zbMATH DE number 6105699