engleski

Structure Functions of Ruled Surfaces with Null Rulings

In this paper we analyse ruled surfaces in Lorentz-Minkowski space in terms of their structure functions. 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.g. proving the classical Dini-Beltrami theorem which states (in Euclidean space) that a ruled skew Weingarten surface is a piece of a helicoidal surface. 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 analyse helicoidal surfaces among Weingarten null-ruled surfaces in terms of their structure functions.

Minkowski space, isometry, ruled surface, B-scroll

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