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The pedal surfaces of $$(1,2)$$-congruences with a one-parameter set of ellipses. (English) Zbl 0898.51015
In 3-dimensional space, among surfaces of the 4th order with a nodal line [see G. Salmon, ‘A treatise on the analytic geometry of three dimensions, Vol. II, Chelsea Publ. Co., New York (1965); see the 5th ed. (1915; JFM 45.0807.05)] those through the absolute conic form a special class which contains the pedal surfaces of $$(1,2)$$-congruences. The author classifies one class of these surfaces with regard to the number and types of their real singular points.
##### MSC:
 51N20 Euclidean analytic geometry 53A05 Surfaces in Euclidean and related spaces
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