On the curvature ODE associated to the Ricci flow

Bhattacharya, Atreyee (2015) On the curvature ODE associated to the Ricci flow. In: GEOMETRIAE DEDICATA, 175 (1). pp. 189-209.

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Abstract

In the vector space of algebraic curvature operators we study the reaction ODE which is associated to the evolution equation of the Riemann curvature operator along the Ricci flow. More precisely, we give a partial classification of the zeros of this ODE up to suitable normalization and analyze the stability of a special class of zeros of the same. In particular, we show that the ODE is unstable near the curvature operators of the Riemannian product spaces where is an Einstein (locally) symmetric space of compact type and not a spherical space form when .

Item Type:	Journal Article
Publication:	GEOMETRIAE DEDICATA
Publisher:	SPRINGER
Additional Information:	Copy right for this article belongs to the SPRINGER, VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
Keywords:	The curvature ODE; Ricci flow; Curvature operator; Stability of curvature
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	23 Apr 2015 07:40
Last Modified:	23 Apr 2015 07:40
URI:	http://eprints.iisc.ac.in/id/eprint/51356

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