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...
Riemann maps in almost complex manifolds
We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.
Riemann Surfaces with Shortest Geodesic of Maximal Length.
Riemannian convexity.
Riemannian convexity in programming. II.
Riemannian foliations on Manifolds with non-negative curvature.
Riemannian foliations with parallel or harmonic basic forms
In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.
Riemannian Isometry Groups Containing Transitive Reductive Subgroups.
Riemannian Manifoids Diffeomorphic to the Complex Projective Space.
Riemannian manifolds admitting certain conformal changes of metric
Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix
Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures , which are not locally homogeneous, in general.
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.
Riemannian manifolds with bounded Dirichlet finite polyharmonic functions
Riemannian Manifolds with Flat Ends.
Riemannian Manifolds with General Symmetries.
Riemannian manifolds with many Killing vector fields
Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion
The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S2 associated to the...
Riemannian metrics with harmonic curvature on 2-sphere bundles over compact surfaces