Minimizability of developable Riemannian foliations

被引:1
|
作者
Nozawa, Hiraku [1 ]
机构
[1] Ecole Normale Super Lyon, Unite Mathemat Pures & Appl, F-69364 Lyon 07, France
关键词
Riemannian foliations; Taut foliations; Secondary characteristic classes;
D O I
10.1007/s10455-010-9203-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let (M, F) be a closed manifold with a Riemannian foliation. We show that the secondary characteristic classes of the Molino's commuting sheaf of (M, F) vanish if (M, F) is developable and pi(1)M is of polynomial growth. By theorems of Alvarez Lopez in (Alvarez Lopez, Ann. Global Anal. Geom., 10: 179-194, 1992) and (Alvarez Lopez, Ann. Pol. Math., 64: 253-265, 1996), our result implies that (M, F) is minimizable under the same conditions. As a corollary, we show that (M, F) is minimizable if F is of codimension 2 and pi(1M) is of polynomial growth.
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页码:119 / 133
页数:15
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