Sentence examples for flat connection from inspiring English sources
On the tangent bundle ({T} G) there exists a canonical flat connection (nabla ).
The construction of the geodesic loop associated with a flat connection is due to Kikkawa [24] and Sabinin [49].
It can be seen that each flat connection on a neighbourhood of a point comes from a local loop, called the geodesic loop of the connection.
In the case of the lower reservoir there is a nearby access road, so only a short and flat connection to it is necessary.
For example, it is possible to produce a one-sided flat connection, which is not producible with any other joining technology.
It can be shown that the necessary condition for an infinitesimal loop (which is also sufficient in the case of analytic loops) to be a geodesic loop of a flat connection is that it should satisfy the right alternative property.
The adjective "flat" here is supposed to reflect the fact that these are the tangent structures to general flat connections.
This induces a symplectic structure for the moduli space of flat connections with boundary holonomies lying in prescribed conjugacy classes.
Moreover, under an additional geometrical hypothesis, we show that the transformationΦSestablishes an equivalence of categories between coherent DX-modules, modulo flat connections, and coherent DY-modules with regular singularities along an involutive manifoldV, modulo flat connections (hereVis determined by the geometry of the correspondence).
It would be fair to say that most of the constructions and results on Sabinin algebras mentioned in the previous section were the product of a quest for a Lie theory of flat connections.
In an article published by Zipprich et al., 10 implant systems that used either conical or flat-to-flat connections were compared relative to their dynamic lateral load responses under simulated clinical conditions.
