On Fibrations with Flat Fibers
نویسندگان
چکیده
We describe the pairs (p, n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.
منابع مشابه
On Fibrations Whose Geometric Fibers Are Nonreduced
We give a bound on embedding dimensions of geometric generic fibers in terms of the dimension of the base, for fibrations in positive characteristic. This generalizes the well-known fact that for fibrations over curves, the geometric generic fiber is reduced. We illustrate our results with Fermat hypersurfaces and genus one curves.
متن کاملTorus Fibrations of Calabi-yau Hypersurfaces in Toric Varieties
1. Introduction. Strominger, Yau, and Zaslow [SYZ] conjectured that any Calabi-Yau manifold X having a mirror partner X ∨ should admit a special Lagrangian fi-bration π : X → B. (A mathematical account of their construction can be found in [M].) If so, the mirror manifold X ∨ is obtained by finding some suitable compactifi-cation of the moduli space of flat U(1)-bundles along the nonsingular fi...
متن کاملFree Vibration Analysis of Variable Stiffness Composite Laminates with Flat and Folded Shapes
In this article, free vibration analysis of variable stiffness composite laminate (VSCL) plates with flat and folded shapes is studied. In order to consider the concept of variable stiffness, in each layer of these composite laminated plates, the curvilinear fibers are used instead of straight fibers. The analysis is based on a semi-analytical finite strip method which follows classical laminat...
متن کاملGeneric fibrations around multiple fibers
Given some type of fibration on a 4-manifold X with a torus regular fiber T , we may produce a new 4-manifold XT by performing torus surgery on T . There is a natural way to extend the fibration to XT , but a multiple fiber (nongeneric) singularity is introduced. We construct explicit generic fibrations (with only indefinite fold singularities) in a neighborhood of this multiple fiber. As an ap...
متن کاملEquivalence Problem for Second Order Pde and Double Fibration as a Flat Model Space
Abstract. In this paper, we consider an equivalence problem of second order partially differential equations (PDE) and a duality of the flat differential equation. For the equivalence problem, explicit form of invariants (curvatures) are given. In particular, if all of the curvatures vanish, then PDE are equivalent to the flat equation. We also investigate a duality associated with the flat equ...
متن کامل