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Constant angle property and canonical principal directions for surfaces in \(\mathbb M^2(c)\times\mathbb R_1\). (English) Zbl 1277.53018
In recent years a lot of progress has been made in the study of surfaces in a product space of a constant curvature surface with a real line. Of course, by changing the sign of the metric on the line component, one obtains an example of a Lorentzian space. In the paper under review, the authors study similar questions for space-like and time-like surfaces in the Lorentzian space obtained in this way. In these spaces, the authors obtain a classification of constant angle surfaces and surfaces with a principal canonical direction. Most of the statements of the theorems and its proofs are quite similar to the Riemannian case.

MSC:
53B25 Local submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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