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Scalar field on a sphere. (English. Russian original) Zbl 0579.53011
Sov. Math. 26, No. 9, 53-64 (1982); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1982, No. 9(244), 40-48 (1982).
The authors investigate geometric interpretations of a scalar field u on the sphere. Section 1 is devoted to the study of the first indicatrix of the function u, i.e., the envelope of the two-parameter family of planes \(n\cdot r-u=0\). Section 2 deals with the second indicatrix of u, i.e., the family of concentric quadrics (with center at the origin) which have contact of order two with the family of planes. Sections 3 and 4 deal with line congruences related to the second indicatrix.
53A35 Non-Euclidean differential geometry
53B05 Linear and affine connections