What is Complex 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 complex conjugate of a complex vector space V...

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

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, 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...

In mathematics, a vector bundle is said to be flat if it is endowed with a linear connection with vanishing curvature, i.e. a flat connection.