On existence of special nets in affinely connected spaces (Q1902758)

Let \((V^n, g)\) be an \(n\)-dimensional Riemannian space with metric tensor \(g\). If \((V^n, g)\) admits a coordinate net such that both the matrix of components of the tensor \(g\) and the matrix of bivector components of the Riemann-Christoffel tensor have diagonal forms, then the coordinate net is said to be biorthogonal. The author proves that biorthogonal nets exists, and the set of such nets depends on \(n\) \((n- 1)\) functions of two variables. She also proves a similar existence theorem for so-called biconjugate nets in an affinely connected space.