An explicit classification of the spaces in the title is given. The resulting spaces are locally products or locally warped products of the real line and two-dimensional spaces of constant curvature.
This paper is motivated by the open problem whether a three-dimensional curvature homogeneous hypersurface of a real space form is locally homogeneous or not. We give some partial positive answers.
We prove that a three-dimensional almost Kenmotsu manifold is locally symmetric if and only if it is locally isometric to either the hyperbolic space ℍ³(-1) or the Riemannian product ℍ²(-4)×ℝ.
We consider a unit speed timelike curve in Minkowski 4-space and denote the Frenet frame of by . We say that is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction of . In this work we study those helices where the function is constant and we give different characterizations of such curves.
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does not satisfy...
In this paper we study the topological and metric rigidity of hypersurfaces in , the -dimensional hyperbolic space of sectional curvature . We find conditions to ensure a complete connected oriented hypersurface in to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.
In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].