On \(L^ 2\) and \(L^ 3\) (Q917934)

Two results are proposed: a) A closed convex curve in the Minkowski 2- space has at least four light-like tangents. b) A curve in Minkowski 3- space having light-like tangents everywhere must be (a piece of) a straight line. [Reviewer's remark: The first result is true for any closed smooth curve in the Minkowski plane and very easy to see. In contrast to the statement of the author it does not provide a suitable analogon of the four-vertex- theorem, because for closed convex curves in the Minkowski plane the existence of four extrema of the curvature can be shown though it is not defined everywhere. The second proposition is wrong.].