Prime Geodesic
In
mathematics
, a
prime geodesic
on a
hyperbolic
surface
is a primitive closed
geodesic
, i.e. a geodesic which is a
closed curve
that traces out its image exactly once. If the surface is given by the quotient of the
hyperbolic plane
by a
Fuchsian group
Γ, then there is a
1-1 correspondence
between prime geodesics and primitive hyperbolic conjugacy classes {γ} in Γ. Such geodesics are called prime geodesics because they obey an asymptotic distribution law similar to the
prime number theorem
. See also:
Modular group Gamma
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