Isotropic space form Riemannian submersions
Makaleler > Tam Makale · 2025
Yazarlar: Müge Sert, Feyza Esra ERDOĞAN
Filomat, Uluslararası, Wos, 2025, cilt 39, ss 6711-6722
DOI: 10.2298/fil2519711s
Özet
We introduce the notion of isotropic space form submersions between Riemannian manifolds in this paper. We begin with a concrete example to demonstrate this new concept. We then characterize isotropic space form submersions in terms of O'Neill's tensor field, \tilde{T} , and explore some relationships between the sectional curvatures of the base manifold and the total manifold. Particularly, considering an isotropic lift \tilde{M}^{\ell} (where \ell \ge 3 ) into a space form \tilde{N}^{n+p}({?c}) with constant ?c sectional curvature, we demonstrate that the \tilde{T} -fundamental tensor of \tilde{N}^{\ell+p} with respect to \tilde{M}^{\ell} is parallel if the mean curvature vector of \tilde{M}^{\ell} is parallel and the sectional curvature \tilde{K} of \tilde{N}^{\ell+p} satisfies a given inequality. Accordingly, \tilde{N}^{\ell+p} is a space form with lift.