标题： 一个余维一的叶状$(α,β)$-空间的积分公式 显示英文标题

标题： Integral formula for codimension-one foliated $(α,β)$-spaces

摘要： 积分公式对于叶状黎曼流形为存在具有给定几何性质的叶状结构或紧致叶提供了障碍。 最近，我们将一个新的黎曼度量与余维一的叶状Finsler空间相关联，并证明了通用和Randers空间的积分公式。 在本文中，我们研究这种度量对于更广泛的余维一叶状$(\alpha,\beta)$-空间，并将其体现在一组可以视为与$\alpha$相关联的扰动度量中。 对于此类度量，我们计算叶子的Weingarten算子并推导出Reeb类型的积分公式，该公式可用于$(\alpha,\beta)$-空间，例如Randers和Kropina空间。 显示英文摘要

摘要： Integral formulae for foliated Riemannian manifolds provide obstructions for existence of foliations or compact leaves of them with given geometric properties. Recently, we associated a new Riemannian metric to a codimension-one foliated Finsler space and proved integral formulae for general and for Randers spaces. In the paper, we study this metric for a wider class of codimension-one foliated $(\alpha,\beta)$-spaces and embody it in a set of metrics that can be viewed as a perturbed metric associated with $\alpha$. For such metrics we calculate the Weingarten operator of the leaves and deduce the Reeb type integral formula, which can be used for $(\alpha,\beta)$-spaces, e.g. Randers and Kropina spaces.