On the Curvature ODE associated to the Ricci flow

Atreyee Bhattacharya

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arXiv · 1310.4618

On the Curvature ODE associated to the Ricci flow

Atreyee Bhattacharya

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Abstract

In the vector space of algebraic curvature operators we study the reaction ODE $$\frac{dR}{dt} = R^2+R^{#}= Q(R)$$ which is associated to the evolution equation of the Riemann curvature oper- ator along the Ricci flow. More precisely, we analyze the stability of a special class of zeros of this ODE up to suitable normalization. In particular, we show that the ODE is unstable near the curvature operators of the Riemannian product spaces $M \times \mathbb{R}^k, \ k \geq 0$ where $M$ is an Einstein (locally) symmetric space of compact type and not a spherical space form when $k = 0.$

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Atreyee Bhattacharya. 2013-10-17. On the Curvature ODE associated to the Ricci flow. https://arxiv.org/abs/1310.4618

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