| In this thesis we consider a conjecture of Martin Hotine on triply orthogonal coordinate systems and their use in differential geodesy. The principal mathematical tools employed are conformal mappings between Riemannian spaces, orthogonal ennuples, and Ricci rotation coefficients.;The thesis consists of four chapters. The first is a brief survey of geodesy and its interaction with mathematics. Chapter II and III are devoted to some mathematical preliminaries on conformal geometry necessary to our discussion of Hotine's conjecture. Many of these topics are not readily accessible in the literature, and have been reformulated and given concise proofs. These include a new proof of the generalized Dupin theorem, a new derivation of the Cayley-Darboux equation, and a critical examination of criteria for conformal flatness. Chapter IV contains a detailed discussion of Hotine's conjecture and its refutation. |
