On the structure of almost Einstein manifolds

Details On the structure of almost Einstein manifolds On the structure of almost Einstein manifolds

2012-02-14

arxiv.org/abs/1202.2912v1

Mathematics

Differential Geometry

40 pages, 3 figures

Scientific paper

In this paper, we study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the $L^1$-sense, Ricci curvatures are bounded from below at the initial time. Under the non-collapsed condition, we show that the limit space of a sequence of almost Einstein manifolds has most properties which is known for the limit space of Einstein manifolds. As applications, we can apply our structure results to study the properties of K\"ahler manifolds.

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