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arXiv · 1607.00989

Integral formula for codimension-one foliated $(\alpha,\beta)$-spaces

Vladimir Rovenski
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Abstract

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.

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Vladimir Rovenski. 2016-07-04. Integral formula for codimension-one foliated $(\alpha,\beta)$-spaces. https://arxiv.org/abs/1607.00989

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