On Riemannian manifolds satisfying a certain curvature condition imposed on the Weyl curvature tensor
On Riemannian tangent bundles.
On sectional and bisectional curvature of the -umbilical submanifolds.
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-invariant submanifolds of -cosymplectic manifolds.
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 2-Dimensional Hermitian Manifolds.
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 analytical manifolds of constant sectional curvature.
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 class of nearly conformally symmetric manifolds
On some class of pseudosymmetric warped products
We present curvature properties of pseudosymmetry type of some warped products of semi-Riemannian spaces of constant curvature.
On some C-totally real submanifolds in a space with Sasakian 3-structure
On some curvature tensors of complex analytic and locally decomposable Riemannian spaces with -connection.
On some flat connection associated with locally symmetric surface
For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on some principal fibre bundle P(M,G). Associated with - satisfying some particular conditions - local basis of TM local connection form of such a connection is an R(G)-valued 1-form build from the dual basis ω1, ω2 and from the local connection form ω of ▽. The structural equations of (M,∇) are equivalent to the condition dΩ-Ω∧Ω=0. This work...
On some generalisation of recurrent manifolds.