论文标题
$ l^2 $ - 欧拉级的叶子'
The $L^2$-norm of the Euler class for Foliations on closed irreducible Riemannian 3-Manifolds
论文作者
论文摘要
$ l^2 $ - 欧拉类$ e（\ cal f）$的$ l^2 $ - 横向定向的叶子的$ e（\ cal f）$的condimension o $ \ cal f $ of Condimension One的定义，在三维不可约束的不可约束的不可约束的riemannian 3-maniian 3-manifold $ m^3 $中，将$ cuniftive us $ cunip bunius us uster and uster ustius ustius uster和mor uster cunip an叶子平均曲率的模量。结果，我们得到的是，$ h^2（m^3）$的组中只有许多有限的cohomolo \ g级类，这些类别可以由Euler类$ e（\ cal f）$的二维式叶子$ \ cal f $的欧拉类$ e（\ cal f）$实现。
An upper bound for the $L^2$- norm of the Euler class $e(\cal F)$ of an arbitrary transversally orientable foliation $\cal F$ of codimension one, defined on a three-dimensional closed irreducible orientable Riemannian 3-manifold $M^3$ is given in terms of constants bounding the volume, the radius of injectivity, the sectional curvature of $M^3$ and the modulus of mean curvature of the leaves. As a consequence we get that only finitely many cohomolo\-gical classes of the group $H^2(M^3)$ that can be realized by the Euler class $e(\cal F)$ of a two-dimensional transversely oriented foliation $\cal F $ whose leaves have the modulus of mean curvature which is bounded above by the fixed constant $H_0$.
