  Space curve motion describes dynamics of material defects or interfaces, can
be found in image processing or vortex dynamics. This article analyses some
properties of space curves evolved by the curve shortening flow. In contrast to
the classical case of shrinking planar curves, space curves do not obey the
Avoidance principle in general. They can lose their convexity or develop
non-circular singularities even if they are simple. In the first part of the
text, we show that even though the convexity of space curves is not preserved
during the motion, their orthogonal projections remain convex. In the second
part, the Avoidance principle for spherical curves under the curve shortening
flow in $\mathbb{R}^3$ is shown by generalizing the arguments developed by
Hamilton and Gage.
