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On the inner curvature of the second fundamental form of

Ayse Altin

Abstract


Let M be a ruled surface in Minkowski three space. Let H be the mean curvature and KII denote the inner curvature of second fundamental form. It is first pointed out that if KII = H for ruled surface with a nonnull directrix curve and nonnull ruling curve, then M is minimal surface. However if directrix curve or ruling curve is null the surface is not minimal, KII and H are constant and equal along each ruling. Linear combination of KII and H are constant along each ruling for ruled surface with a nonnull directrix curve and nonnull ruling curve is studied. In particular the only ruled surface with curvature of the second fundamental form vanishing is a piece of a helicoid.

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