Algebraic surfaces with an infinite set of planes of oblique symmetry. I (Q1814063)

The author proves some theorems describing equations of a noncylindrical algebraic surface in an Euclidean space which has infinite set of planes of oblique (in particular orthogonal) symmetry. The main goal of the paper is to give detailed (in individual cases, modified) proofs of the results of two early papers of the author [Differ. Geom. Mnogoobrazij Figur. 7, 34-39 (1976; Zbl 0429.51011) and Ukr. Geom. Sb. 20, 35-46 (1977; Zbl 0429.51012)]. Some results of invariant theory of reflection groups are used in the proofs of the theorems of the reviewed paper.