What is Flat vector bundle?

In mathematics, a frame bundle is a principal fiber bundle F associated to any vector bundle E. The fiber of F over a point x is the set of all...

In mathematics, the canonical bundle of a non-singular algebraic variety V {\displaystyle V}...

In mathematics, a complex vector bundle is a vector bundle whose fibers are complex vector spaces. Any complex vector bundle can be viewed as a real vector bundle through the...

In mathematics, and especially complex geometry, the holomorphic tangent bundle of a complex manifold M...

A torus bundle, in the sub-field of geometric topology in mathematics, is a kind of surface bundle over the circle, which in turn is a class of three-manifolds.

In differential geometry, the tensor product of vector bundles E, F is a vector bundle, denoted by E ⊗ F, whose fiber over a point...

In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect"...

In mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space; thus, given a real vector bundle π: E →B, an orientation...

In mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle from a given base space, fiber and a suitable set of transition functions. The theorem...

In mathematics, particularly differential topology, the secondary vector bundle structurerefers to the natural vector bundle structure on the total space TE of the tangent bundle of a smooth vector bundle...