Behavior of distant maximal geodesies in 2-dimensional manifolds 7
the two following situations may occur.
(i) [a\,b\] n [02^2] =
*n
which case p\ and pi are said to be
independent.
(ii) [ai,b\] n [02,^2] is a nonempty interval / * [2i,Z?;] for / = 1,2, in
which case/?i and/?2 are said to /m&.
P\ and^2 mz independent. p\ and pi link.
1.4. Definition. A proper transversal immersion of some (not necessarily
compact) closed interval of R into M is called a semi-regular arc when the set of
double points of a is totally ordered by the previously defined order relation.
A semi-regular arc
In other words, setting ~n{a) := n+(cc) + n_(a) and for all n e N U {00}
denoting by [n] the set of all integers / such that 1 i n, the proper transversal
immersion a is said to be semi-regular when there exists a sequence of closed
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