2016/07/04 by Vladimir Rovenski, Rovenski, Vladimir
Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1607.00989
openalex publication_date 2016/07/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
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 (α,β)-spaces and embody it in a set of metrics that can be viewed as a perturbed metric associated with α. For such metrics we calculate the Weingarten operator of the leaves and deduce the Reeb type integral formula, which can be used for (α,β)-spaces, e.g. Randers and Kropina spaces.