Submersje konforemne o włóknach umbilikalnych

Abstract

Conformal submersions are natural generalisation of Riemannian submersions, introduced by O'Neill (1966). Using methods of Riemannian geometry, curvature relations between the domain and the image of such submersion were examined. Integral formulae were obtained and some existence conditions for conformal submersions with totally umbilical fibers were derived. Also, natural constructions and examples of those mappings were sought, without exploiting their obvious relation to Riemannian submersions. The above research may be summarized as investigating foliations and distributions of special extrinsic geometry, considered on Riemannian manifolds.