H-transformations in Riemannian spaces

Abstract

A Riemannian space Vn (n = mr), equipped with an integrable regular H-structure isomorphic to a hypercomplex algebra h (dim h = r), is considered as a real realization of a hypercomplex manifold\(\mathop V\limits^* _m \) over the algebra h. The geometry of\(\mathop V\limits^* _m \) can be mapped into the geometry of Vn. In particular, with the transformations of\(\mathop V\limits^* _m \) are associated H transformations (preserving the H-structure of the space) in Vn. The H-conformal and the H-projective transformations of Vn are investigated.