Special affine curvature, also known as the equiaffine curvature or affine curvature, is a particular type of curvature that is defined on a plane curve...

connection on the frame bundle. The main invariants of an affine connection are its torsion and its curvature. The torsion measures how closely the Lie bracket...

& Sasaki 1994). If ∇ {\displaystyle \nabla } denotes an affine connection, then the curvature tensor R {\displaystyle R} is the (1,3)-tensor defined by...

complete set of affine structural invariants of the curve. In the plane, this gives a single scalar invariant, the affine curvature of the curve. The...

with an affine connection. It is a central mathematical tool in the theory of general relativity, the modern theory of gravity. The curvature of spacetime...

the Euler class in terms of the curvature. The conjecture is known to hold in several special cases: when a compact affine manifold is 2-dimensional (as...

which is homeomorphic to an open disk. Viewing the plane as an affine space produces the affine plane, which lacks a notion of distance but preserves the notion...

geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using...

Look up affine in Wiktionary, the free dictionary. The principal curvature-based region detector, also called PCBR is a feature detector used in the fields...

characterised by the property of having vanishing geodesic curvature. More generally, in the presence of an affine connection, a geodesic is defined to be a curve...