On Riemannian manifolds satisfying a certain curvature condition imposed on the Weyl curvature tensor
On sectional curvature of a Riemannian manifold with semi-symmetric metric connection
We prove that if the sectional curvature of an n-dimensional pseudo-symmetric manifold with semi-symmetric metric connection is independent of the orientation chosen then the generator of such a manifold is gradient and also such a manifold is subprojective in the sense of Kagan.
On Sectional Curvature of Indefinite Metrics.
On Sectional Curvature of Indefinite Metrics, II.
On semi-Riemannian manifolds satisfying some conformally invariant curvature condition
We investigate semi-Riemannian manifolds with pseudosymmetric Weyl curvature tensor satisfying some additional condition imposed on their curvature tensor. Among other things we prove that the so-called Roter type equation holds on such manifolds. We present applications of our results to hypersurfaces in semi-Riemannian space forms, as well as to 4-dimensional warped products.
On some Akivis - Goldberg Type Metrics
On some Akivis-Goldberg type metrics.
On some algebraic identities and the exterior product of double forms
We use the exterior product of double forms to free from coordinates celebrated classical results of linear algebra about matrices and bilinear forms namely Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and Jacobi’s formula for the determinant. This coordinate free formalism is then used to easily generalize the previous results to higher multilinear forms namely to double forms. In particular, we show that the Cayley-Hamilton theorem once applied to the second...
On some class of hypersurfaces with three distinct principal curvatures
We investigate hypersurfaces M in spaces of constant curvature with some special minimal polynomial of the second fundamental tensor H of third degree. We present a curvature characterization of pseudosymmetry type for such hypersurfaces. We also prove that if such a hypersurface is a manifold with pseudosymmetric Weyl tensor then it must be pseudosymmetric.
On some curvature tensors of complex analytic and locally decomposable Riemannian spaces with -connection.
On some generalisation of recurrent manifolds.
On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms
Solutions of the P. J. Ryan problem as well as investigations of curvature properties of Cartan hypersurfaces and Ricci-pseudosymmetric hypersurfaces lead to curvature identities holding on every hypersurface M isometrically immersed in a semi-Riemannian space form. These identities, under some assumptions, give rises to new generalized Einstein metric conditions on M. We investigate hypersurfaces satisfying such curvature conditions.
On some Hypersurfaces of a Recurrent Riemannian Space
On some properties of a Riemannian space with constant scalar curvature
On some pseudo-symmetric Riemann spaces.
On some Riemannian manifolds admitting a metric semi-symmetric connection
On some type of curvature conditions
In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.
On space-times with commutative parings of vector fields.
On subprojective transformations.
On symmetric Riemannian manifolds.