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Ruled surfaces with null curves and Frenet frame in pseudo-sphere and pseudo-hyperbolic space. (English) Zbl 1515.53060

Summary: In this paper, we construct Frenet frame fields along a null curve when it is not a bi-null Cartan curve in a pseudo-hyperbolic space with index 2 and pseudo-sphere with index 2, respectively. Also, we find ruled surfaces with the above null curves which have non-diagonalizable shape operators, constant mean curvatures and constant scalar curvatures.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
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