On the Riemannian curvature tensor of an almost-product manifold
On the symmetry classes of the first covariant derivatives of tensor fields.
On totally umbilical surfaces in some Riemannian spaces
On weakly and pseudo concircular symmetric structures on a Riemannian manifold
In this paper, we examine the properties of hypersurfaces of weakly and pseudo concircular symmetric manifolds and we give an example for these manifolds.
On Weakly -Symmetric Manifolds
The object of the present paper is to study weakly -symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly -symmetric manifold both the decompositions are weakly Ricci symmetric.
Optimal inequalities characterising quasi-umbilical submanifolds.
Product-concircular curvature tensor.
Projectively invariant distances for affine and projective structures
Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures
We study properties of pseudo-Riemannian metrics corresponding to Monge-Ampère structures on four dimensional . We describe a family of Ricci flat solutions, which are parametrized by six coefficients satisfying the Plücker embedding equation. We also focus on pullbacks of the pseudo-metrics on two dimensional , and describe the corresponding Hessian structures.
Pseudo-symmetric contact 3-manifolds III
A trans-Sasakian 3-manifold is pseudo-symmetric if and only if it is η-Einstein. In particular, a quasi-Sasakian 3-manifold is pseudo-symmetric if and only if it is a coKähler manifold or a homothetic Sasakian manifold. Some examples of non-Sasakian pseudo-symmetric contact 3-manifolds are exhibited.
Quasi-Einstein hypersurfaces in semi-Riemannian space forms
We investigate curvature properties of hypersurfaces of a semi-Riemannian space form satisfying R·C = LQ(S,C), which is a curvature condition of pseudosymmetry type. We prove that under some additional assumptions the ambient space of such hypersurfaces must be semi-Euclidean and that they are quasi-Einstein Ricci-semisymmetric manifolds.
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...