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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.

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