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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.43, no.1, pp.809-831, 2020 (SCI-Expanded)
In the present paper, we introduce a new kind of Riemannian submersion such that the fibers of such submersion are generic submanifolds in the sense of Ronsse that we call generic submersion. Some examples are given for generic submersion. Necessary and sufficient conditions are found for the integrability and totally geodesicness of the distributions which are mentioned in the definition. The geometry of the fibers is investigated. New results are obtained by considering the parallelism condition of canonical structures.