Characteristic classes of almost-flag structures
Let \(F=(F_ 1,...,F_ k)\) be a sequence of sub-fiber bundles of the tangent bundle T(V) of a smooth manifold V. Let this sequence be totally ordered by inclusion and suppose that \(co\dim (F_ 1)=q_ 1\). The frames of \(T(V)/F_ 1\), adapted to F, form a G-principal sub-fiber bundle of the \(GL(q_ 1;{\mathbb{R}})\)-bundle of all frames. If \(I(GL(q_ 1;{\mathbb{R}}))\to I(G)\) is the natural restriction morphism \(\rho\), then the Chern-Weil morphism of \(T(V)/F_ 1\) is zero on the kernel of \(\rho\). This vanishing phenomenon allows the author to construct secondary classes for F, applying the difference operator theory of Chern-Bott. Taking F to be a flag-structure and X an infinitesimal automorphism of F, the author generalizes the two residue theorems of \textit{J. L. Heitsch} [Ann. Math., II. Ser. 108, 421-460 (1978; Zbl 0398.57007)] using the connection deformation method of \textit{D. Lehmann} [Ann. Inst. Fourier 24, No.3, 267-306 (1974; Zbl 0268.57009)].
sequence of sub-fiber bundles of the tangent bundle of a smooth manifold
difference operator theory of Chern-Bott
scientific article; zbMATH DE number 4117469