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Classification of constant angle surfaces in a warped product. (English) Zbl 1228.53021
In the last years, several studies appeared on surfaces forming a constant angle with a vector field in different ambient manifolds. A strong motivation for these works consists in possible physical applications, for instance in the theory of liquid crystals in a Euclidean ambient space.
The present paper is devoted to the above problem in a three-dimensional warped product space with Euclidean factors. The main result is a classification theorem which yields several very interesting examples: rotational surfaces of constant angle, flat and minimal constant angle surfaces, and constant angle surfaces with harmonic height functions.

53B25 Local submanifolds
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