A New Approach to the Theory of the Riemann Space
A new characterization of -stable hypersurfaces in space forms
In this paper we study the -stability of closed hypersurfaces with constant -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the -th mean curvature.
A New Formula for the Shape Operator of a Geodesic Sphere and Its Applications.
A note on a hermitian analog of Einstein spaces
A Note on Billiard Systems in Finsler Plane with Elliptic Indicatrices
A Note on Curvature-like Invariants of Some Connections on Locally Decomposable Spaces
A note on geodesic mappings of pseudosymmetric Riemannian manifolds
A note on homogeneous production models
A Note on Rakić Duality Principle for Osserman Manifolds
A note on the Riemann curvature tensor
A note on the volume of -Einstein manifolds with skew-torsion
We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the first variation of the volume in terms of the corresponding scalar curvature. This generalizes a result of M. Ville [Vil] related with the first variation of the volume on a compact Einstein manifold.
A particular conformally symmetric space
A principle involving the variation of the metric tensor in a stationary space-time of general relativity
A property of Wallach's flag manifolds
In this note we study the Ledger conditions on the families of flag manifold , , constructed by N. R. Wallach in (Wallach, N. R., Compact homogeneous Riemannian manifols with strictly positive curvature, Ann. of Math. 96 (1972), 276–293.). In both cases, we conclude that every member of the both families of Riemannian flag manifolds is a D’Atri space if and only if it is naturally reductive. Therefore, we finish the study of made by D’Atri and Nickerson in (D’Atri, J. E., Nickerson, H. K., Geodesic...
A property on geodesic mappings of pseudo-symmetric Riemannian manifolds.
A propos de la conjecture de la balle liquide en relativité générale
A remark on algebraic identities for the covariant derivative of the curvature tensor
A Riemann-Lagrange geometrization for metrical multi-time Lagrange spaces.
A scalar geodesic deviation equation and a phase theorem.
A second-order identity for the Riemann tensor and applications
A second-order differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed. The new structure of K-recurrency naturally emerges from an invariance property of an old identity due to Lovelock.