Classes caractéristiques non triviales des feuilles de sous- feuilletages localement homogènes. (Non-trivial characteristic classes of leaves of locally homogeneous subfoliations)
Let M be a differential manifold and \((F_ 1,F_ 2)\) be a couple of codimension \(q_ i\) foliations on M such that each leaf of \(F_ 1\) contains leaves of \(F_ 2\). The couple \((F_ 1,F_ 2)\) is called a subfoliation of codimension \((q_ 1,q_ 2)\) on M. Each pair \((L_ 1,L_ 2)\) of leaves of \(F_ i\) such that \(L_ 2\subset L_ 1\) is said to be a leaf of \((F_ 1,F_ 2)\). The author describes the computation of the secondary characteristic classes and of the holonomy classes for the leaves of locally homogeneous subfoliations. As an application, the author gives some examples of locally homogeneous subfoliations with non- trivial secondary characteristic classes, respectively holonomy classes of a leaf \((L_ 1,L_ 2)\), which cannot be obtained if one considers each leaf separately.
scientific article; zbMATH DE number 4084583