Definition
If E0, E1, ..., Ek are vector bundles on a smooth manifold M (usually taken to be compact), then a differential complex is a sequence
of differential operators between the sheaves of sections of the Ei such that Pi+1 o Pi=0. A differential complex is elliptic if the sequence of symbols
is exact outside of the zero section. Here π is the projection of the cotangent bundle T*M to M, and π* is the pullback of a vector bundle.
Read more about this topic: Elliptic Complex
Famous quotes containing the word definition:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)