RIEMANNIAN SUBMERSIONS FROM RIEMANN SOLITONS

OpenAlex İngilizce

In the present paper, we study a Riemannian submersion π from a Riemann soliton (M1, g, ξ, λ) onto a Riemannian manifold (M2, g ′ ).We first calculate the sectional curvatures of any fibre of π and the base manifold M2.Using them, we give some necessary and sufficient conditions for which the Riemann soliton (M1, g, ξ, λ) is shrinking, steady or expanding.Also, we deal with the potential field ξ of such a Riemann soliton is conformal and obtain some characterizations about the extrinsic vertical and horizontal sectional curvatures of π.