IsClosed(ls)

For a LineString value ls, IsClosed() returns 1 if ls is closed (that
is, its StartPoint() and EndPoint() values are the same). If the
argument is NULL or an empty geometry, the return value is NULL.

For a MultiLineString value ls, IsClosed() returns 1 if ls is closed
(that is, the StartPoint() and EndPoint() values are the same for each
LineString in ls).

IsClosed() returns 0 if ls is not closed.

URL: http://dev.mysql.com/doc/refman/5.5/en/gis-linestring-property-functions.html

