  This note studies Arveson's curvature invariant for d-contractions
specialized to the case d=1 of a single contraction operator on a Hilbert
space. It establishes a formula which gives an easy-to-understand meaning for
the curvature of a single contraction. The formula is applied to give an
example of an operator with nonintegral curvature. Under the additional
hypothesis that the contraction T be "pure", we show that its curvature K(T) is
given by K(T) = - index(T) := -(dim ker T - dim coker T).
