On the structure of almost Einstein manifolds

Tian, Gang¹ ; Wang, Bing²

¹ Department of Mathematics, Princeton University, Princeton, New Jersey 08544; Beijing International Center for Mathematical Research, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
² Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706

Journal of the American Mathematical Society, Tome 28 (2015) no. 4, pp. 1169-1209

Résumé

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, and 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 are known for the limit space of Einstein manifolds. As applications, we can apply our structure results to study the properties of Kähler manifolds.

Détail

DOI : 10.1090/jams/834

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