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In this work we present reparametrization of nondegenerate null scroll as a B-scroll, i. We prove that the curvature of a base curve, which determines the Gaussian and mean curvature of a null scroll, is invariant under such a reparametrization. We also determine a one-parameter family of null curves on null scroll which serve as base curves for this kind of reparametrization.
We are especially interested in ruled surfaces which do not have a Euclidean counterpart, that is, surfaces with null rulings, and in particular, so-called B- scrolls. For ruled surfaces in Lorentz- Minkowski space, we establish relations between their structure functions and curvatures.
Structure functions can be used for e. In Lorentz-Minkowski space, the problem is more complex, due to the different types of surfaces with respect to their inherited metrics. It turns out that all null-ruled surfaces are Weingarten, however their structure functions need not be constant. In this paper we analyze helicoidal surfaces among Weingarten null-ruled surfaces in terms of their structure functions.
Null scrolls, i. In this paper we analyze ruled surfaces in Lorentz-Minkowski space in terms of their structure functions.
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