35 research outputs found
On geodesic mappings in particular class of Roter spaces
We determine a particular class of Roter type warped product manifolds. We
show that every manifold of that class admits a geodesic mapping onto a some
Roter type warped product manifold. Moreover, both geodesically related
manifolds are pseudosymmetric of constant type
Hypersurfaces in spaces of constant curvature satisfying a particular Roter type equation
We investigate hypersurfaces M isometrically immersed in an (n+1)-dimensional
semi-Riemannian space of constant curvature, n > 3, such that the operator A^3,
where A is the shape operator of M, is a linear combination of the operators
A^2 and A and the identity operator Id. The main result states that on the set
U of all points of M at which the square of the Ricci operator of M is not a
linear combination of the Ricci operator and the identity operator, the
Riemann-Christoffel curvature tensor R of M is a linear combination of some
Kulkarni-Nomizu products formed by the metric tensor g, the Ricci tensor S and
the tensor S^2 of M, i.e., the tensor R satisfies on U some Roter type
equation. Moreover, the (0,4)-tensor R.S is on U a linear combination of some
Tachibana tensors formed by the tensors g, S and S^2. In particular, if M is a
hypersurface isometrically immersed in the (n+1)-dimensional Riemannian space
of constant curvature, n > 3, with three distinct principal curvatures and the
Ricci operator with three distinct eigenvalues then the Riemann-Christoffel
curvature tensor R of M also satisfies a Roter type equation of this kind.Comment: arXiv admin note: text overlap with arXiv:1911.0248
A note on almost kähler manifolds
For anyn ≥ 2, we give examples of almost Kähler conformally flat manifoldsM 2n which are not Kähler. We discuss the meaning of these examples in the context of the Goldberg conjecture on almost Kahler manifold