Isometric immersions of warped products - Menani, Gustavo Sylvio de Paula (2024)
The first goal of this work is to present proofs of the decomposition theorems of de Rham, Hiepko, and Tojeiro of Riemannian manifolds as Riemannian products, warped products, and product manifolds endowed with polar metrics, respectively, as well as of the decomposition theorems, due to Moore, Nölker and Tojeiro, respectively, of isometric immersions into space forms of Riemannian products, warped products and product manifolds endowed with polar metrics. The second goal is to present an extension, based on Nölkers theorem, of a result due to do Carmo and Dajczer, according to which a hypersurface of a space form with dimension n ≥ 3 and only two distinct principal curvatures λ and μ with μ = μ(λ) of multiplicity one, must be a rotation hypersurface over a curve