… about Riemannian submersions and warped product … of Riemannian warped product
submersions. In Sect. 4, we derive an optimal vertical Casorati inequality for such submersions. …

… warped product submersion with examples and obtain some … define Riemannian warped
product map and find conditions for a Riemannian map to be Riemannian warped product map. …

… ϕ ₂ (p₂)) is a Riemannian submersion? In this study we defined warped product submersion
and give some examples and also studied basic properties of such as a submersion. and …

… on warped products isometrically immersed in real or complex space forms as Riemannian,
… It is well-known that the Hopf fibration π is a Riemannian submersion such that V = iz spans …

… As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion
\(… \mathbb {R}^2\) given by the projection of a warped product onto the Euclidean plane. …

… Riemannian doubly warped product submersions as a natural generalization of Riemannian
warped product submersions… We study some fundamental properties of such submersions …

… manifold that admits a projective mapping of constant rank that is less than its dimension
is isometric to a twisted product. We will use this fact in order to prove statements of a global …

… warped product manifold into an arbitrary Riemannian manifold ? The study of this fundamental
question on warped product … Hopf fibration π is a Riemannian submersion such that V = …

… In the fifth section, we study various product structures including warped product, twisted
product, oblique warped product, and convolution product on Riemannian manifolds. We also …

… a Riemannian submersion such that V = iz spans the vertical subspaces. Let 0 : M -> CP"^'^^
be an isometric immersion. Then M = TT^^M) is a principal circle bundle over M with totally …