An intrinsic characterization of a class of minimal surfaces in constant curvature manifolds
Let M be a minimal surface in an N-dimensional manifold \(X^ N(c)\) of constant sectional curvature c. Its r-th normal plane is said to be exceptional if a certain condition derived from the structure equations is satisfied. M is called an exceptional minimal surface if all of its normal planes are exceptional. The case M lies fully in \(X^ N(c)\) is considered, namely the case such that for some r the r-th osculating space of M coincides with the tangent space of \(X^ N(c)\) at generic points x of M. Then a sequence of functions \(A^ c_ 1\), \(A^ c_ 2,...\), is constructed on M which characterizes the minimal surface M. When N is odd some relation to the Ricci-Lawson theorem is found [\textit{H. B. Lawson jun.}, Ann. Math., II. Ser. 92, 335-374 (1970; Zbl 0205.520)]. When N is even such surfaces are rigid.
scientific article; zbMATH DE number 4205324