Frame bundle

About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.

Torsions of connections on some natural bundles

Abstract: The natural vector valued l-forms Q on the natural bundles associated with product preserving functors (including the tangent bundle, the bundle of first order k-velocities, the bundle of second order l-velocities and the bundle of linear frames) and on the cotangent bundle are classified. Then, these forms Q are used to study the torsion r = (I', Q) of connections P on the above bundles, where ( 1, -1 is the Frolicher-Nijenhuis bracket.

The partition bundle of type AN-1 (2, 0) theory

Abstract: Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss the nature of the object that generalizes the partition function of a more conventional quantum theory. This object takes its values in a certain complex vector space, which fits together into the total space of a complex vector bundle (the ‘partition bundle’) as the data on the six-manifold is varied in its infinite-dimensional parameter space. In this context, an important role is played by the middle-dimensional intermediate Jacobian of the six-manifold endowed with some additional data (i.e. a symplectic structure, a quadratic form, and a complex structure). We define a certain hermitian vector bundle over this finite-dimensional parameter space. The partition bundle is then given by the pullback of the latter bundle by the map from the parameter space related to the six-manifold to the parameter space related to the intermediate Jacobian.

Seshadri-exceptional foliations

Abstract: The maximal Seshadri number μ(L) of an ample line bundle L on a smooth projective variety X measures the local positivity of the line bundle L at a general point of X By refining the method of Ein-Kuchle-Lazarsfeld, lower bounds on μ(L) are obtained in terms of Ln, n=dim(X), for a class of varieties The main idea is to show that if a certain lower bound is violated, there exists a non-trivial foliation on the variety whose leaves are covered by special curves In a number of examples, one can show that such foliations must be trivial and obtain lower bounds for μ(L) The examples include the hyperplane line bundle on a smooth surface in ℙ3 and ample line bundles on smooth threefolds of Picard number 1

Smoothness of the action of the gauge transformation group on connections

Abstract: The NLF–Lie group structure of the group G of the gauge transformations, defined as the group of sections of the bundle P[G] associated to the principal bundle P(M,G), is discussed. Other current definitions of the group of gauge transformations are shown to admit a nontrivial smooth structure only in the case of compact G. The space C of principal connections, as well, is given the structure of local affine NLF‐manifold, after identifications of connections with sections of a convenient vector bundle on M. Finally, the smoothness of the action of G on C is proved in general. In the case of compact M, the group G becomes a tame Frechet–Lie group and the action a tame smooth action.