For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means fundamental tensor has Lorentzian signature on conic subbundle tangent bundle thus existence cone future-pointing time-like vectors is ensured. The identified (α,β)-Finsler spacetimes are candidates for applications i...

Let (M, g) be an oriented 4-dimensional Riemannian manifold (not necessarily compact). Due to the Hodge-star operator ⋆, we have a decomposition of the bivector bundle ∧2 TM = ∧+ ⊕ ∧− . Here ∧± is the eigen-subbundle for the eigenvalue ±1 of ⋆. The metric g on M induces a metric, denoted by < , >, on the bundle ∧2 TM . Let π : Z = S (∧+) −→ M be the sphere bundle; the fiber over a point m ∈ M p...

A complex b-structure on a manifold M with boundary is an involutive subbundle bT 0,1M of the complexification of bTM with the property that CbTM = bT 0,1M + bT 0,1M as a direct sum; the interior of M is a complex manifold. The complex b-structure determines an elliptic complex of b-operators and induces a rich structure on the boundary of M. We study the cohomology of the indicial complex of t...

We prove that a generic linear cocycle over a minimal base dynamics of finite dimension has the property that the Oseledets splitting with respect to any invariant probability coincides almost everywhere with the finest dominated splitting. Therefore the restriction of the generic cocycle to a subbundle of the finest dominated splitting is uniformly subexponentially quasiconformal. This extends...

The higher order bundles defined by an affine bundle E and a vector pseudofield on E are investigated this paper. The acceleration bundles become nontrivial examples which motivate the above extension. Moreover, the main ideas of our construction can be used as well in other cases. Using affine bundles, a dual theory between Lagrangians and Hamiltonians (via Legendre transformations) is conside...

For Lagrangian subbundles with singularities in symplectic vector bundles, explicit formulas of relation between their residue classes and Maslov classes outside singularities are obtained. Then a Lagrangian subbundle with singularity is constructed where all possible Maslov classes are nonzero but residue classes vanish for dimension > 2 . Moreover, a Lagrangian immersion with singularity is c...

Introduction 1. Schubert subschemes and their desingularizations. 2. Isotropic Schubert calculus and the class of the diagonal. 3. Subbundles intersecting an n-subbundle in dim > k. 4. Q̃-polynomials and their properties. 5. Divided differences and isotropic Gysin maps; orthogonality of Q̃-polynomials. 6. Single Schubert condition. 7. Two Schubert conditions. 8. An operator proof of Proposition 3...

The main result we obtain is that given t N M a TS-subbundle of the generalized Hopf fibration t H2+’cP over a Cauchy-Riemann product M _ cP, i.e. N _ H is a diffeomorphism on fibres and oj= ot, if s is even and N is a closed submanifold tangent to the structure vectors of the canonical 5Zstructure on H then N is a Cauchy-Riemann submanifold whose Chen class is non-vanishing.