标题： 一个余维一叶状$(α,β)$-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： 积分公式用于叶状黎曼流形，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，对于芬斯勒空间 $(M,F)$ 的余维一叶状结构 $\cal F$，我们关联了一个新的黎曼度量 $g$，并证明了 $(M,F)$ 和兰德斯空间（$F=\alpha+\beta$）的积分公式。 在论文中，我们研究了这个度量$g$对于更广泛的余维一叶状$(\alpha,\beta)$-空间，并将其体现在一组度量中，这些度量可以看作是与$\alpha$相关的扰动度量。对于这样的度量，我们计算了（叶层的）$\cal F$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, to a codimension-one foliation $\cal F$ of a Finsler space $(M,F)$ we associated a new Riemannian metric $g$ and proved integral formulae for $(M,F)$ and for Randers spaces ($F=\alpha+\beta$). In the paper, we study this metric $g$ 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 of) $\cal F$ and deduce the Reeb type integral formula, which can be used for $(\alpha,\beta)$-spaces, e.g. Randers and Kropina spaces.