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Given a unital C*-algebra
and a right C*-module
over
, we consider the problem of finding short smooth curves in the sphere
= x ∈
: 〈x, x〉 = 1. Curves in
are measured considering the Finsler metric which consists of the norm of
at each tangent space of
. The initial value problem is solved, for the case when
is a von Neumann algebra and
is selfdual: for any element x 0 ∈
and any tangent vector ν at x 0, there exists a curve γ(t) = e tZ(x 0), Z ∈
, Z* = −Z and ∥Z∥ ≤ π, such...
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