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168 A. AGRACHEV and I. ZELENKO called flat at the point I, if the function t (t) satisfies
 

Summary:  168 A. AGRACHEV and I. ZELENKO
called flat at the point I, if the function t (t) satisfies
(t) = 0
() +
-1
i=-l()
Qi()(t - )i
. (1.1)
Definition 2. The curve : I L(W) of constant (finite) weight is
called flat if it is flat at any point of I.
First, consider the regular curves (recall that the curve () is said to be
regular if the velocity (t) is a nondegenerate quadratic form for any t, see
Sec. I.3 for details). In this case the function t (t) has a simple pole
at t = for any . Then, by definition, the regular curve () is flat at iff
(t) = 0
() + Q-1()
1
t -
. (1.2)
The coordinate version of (1.2) is

  

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Zelenko, Igor - Department of Mathematics, Texas A&M University

 

Collections: Engineering; Mathematics