Regularity Theorems in Riemannian Geometry. II. Harmonic Curvature and the Weyl Tensor.
Relating algebraic properties of the curvature tensor to geometry.
Relations between intrinsic and extrinsic curvatures
R-Geodesics and R-asymptotic lines
Ricci and Casorati principal directions of Chen ideal submanifolds
Ricci-semisymmetric hypersurfaces.
Riemann compatible tensors
Derdziński and Shen's theorem on the restrictions on the Riemann tensor imposed by existence of a Codazzi tensor holds more generally when a Riemann compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity for a new "Codazzi deviation tensor", with a geometric significance. The above general properties are studied, with their implications on Pontryagin forms. Examples are given of manifolds with Riemann...
Riemannian manifolds admitting certain conformal changes of metric
Riemannian manifolds not quasi-isometric to leaves in codimension one foliations
Every open manifold of dimension greater than one has complete Riemannian metrics with bounded geometry such that is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential...
Riemannian manifolds with almost constant scalar curvature.
r-y r2 variedades diferenciables.