Constant curvature ratios in L6

Curves with Constant Curvature Ratios

The notion of a generalized helix in R3, a curve making a constant angle with a fixed direction, can be generalized to higher dimensions in many ways. In [7] the same definition is proposed but in R. In [4] the definition is more restrictive: the fixed direction makes a constant angle with all the vectors of the Frenet frame. It is easy to check that this definition only works in the odd dimens...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Constant Curvature Black Holes

Constant curvature black holes are constructed by identifying points in anti-de Sitter space. In n dimensions, the resulting topology is <×S1, as opposed to the usual < ×Sn−2 Schwarzschild black hole, and the corresponding causal structure is displayed by a (n − 1)−dimensional picture, as opposed to the usual 2-dimensional Kruskal diagram. The five dimensional case, which can be embedded in a C...

Para-Kahler tangent bundles of constant para-holomorphic sectional curvature

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

hypersurfaces with constant mean curvature in a lorentzian space form