A study of horizontally weakly conformal maps and their distributions

The aim of this paper is to consider horizontally weakly conformal maps which have been studied in [P. Baird and J. C. Wood, Harmonic morphisms between Riemannian manifolds, London Mathematical Society Monographs. New Series, 29, The Clarendon Press, Oxford University Press, Oxford, 2003]. We first generalize the results of this book for Euclidean space with arbitrary Riemannian metrics and then we study totally umbilic and totally geodesic integral manifolds of the projection map, when regarded as conformal submersion between Euclidean spaces with arbitrary Riemannian metrics.