Euclidean Submanifolds with Nonparallel Normal Space.
We construct a class of nonsemisymmetric Ricci-semisymmetric warped products. Some manifolds of this class can be locally realized as hypersurfaces of a semi-Euclidean space , n ≥ 5.
Let be a noncompact differentiable manifold and an open proper submanifold endowed with a complete Riemannian metric . We prove that can be extended all over to a complete Riemannian metric having the same growth-type as .
We give the definition of -biminimal submanifolds and derive the equation for -biminimal submanifolds. As an application, we give some examples of -biminimal manifolds. Finally, we consider -minimal hypersurfaces in the product space and derive two rigidity theorems.