Comment on curves in 2- and 3-dimensional Monkowski space.
In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results...
For commuting linear operators we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential...
The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kähler manifolds.
A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature Hr, for some r = 1, ..., n.