Warped product manifolds with p-dimensional base, p=1,2, satisfy some
curvature conditions of pseudosymmetry type. These conditions are formed from
the metric tensor g, the Riemann-Christoffel curvature tensor R, the Ricci
tensor S and the Weyl conformal curvature C of the considered manifolds. The
main result of the paper states that if p=2 and the fibre is a semi-Riemannian
space of constant curvature, if n is greater or equal to 4, then the
(0,6)-tensors R.R - Q(S,R) and C.C of such warped products are proportional to
the (0,6)-tensor Q(g,C) and the tensor C is expressed by a linear combination
of some Kulkarni-Nomizu products formed from the tensors g and S. Thus these
curvature conditions satisfy non-conformally flat non-Einstein warped product
spacetimes (p=2, n=4). We also investigate curvature properties of
pseudosymmetry type of quasi-Einstein manifolds. In particular, we obtain some
curvature property of the Goedel spacetime
The main aim of this paper is to investigate the geometric structures admitting by the Gödel spacetime which produces a new class of semi-Riemannian manifolds. We also consider some extension of Gödel metric.
We present some corrections of a part of the original paper [5, Sec. 4, lines 14 9-15 9 ]. In addition, we give examples of manifolds related to the presented corrections. Further, we denote by S and κ the Ricci tensor and the scalar curvature of the product manifold (M × N , g = g × g), respectively. It is obvious that rank S = rank S and κ = κ on U C ⊂ M × N. Now [5, Eq. (24)] yields on this set rank S − κ n − 1 − (n − 2)L C g ≤ 2.
the overall objective of the ongoing work is to develop the computational environment hyDrO-Path as a flexible tool for forecasting runoff from catchment areas for various hydrometeorological conditions while taking into account the information available on a real-time basis. ensuring the model's operational reliability and reducing the uncertainty of generated forecasts is accomplished through the adjustment of both the internal structure of the model and the spatial representation of the computational grid to the physiographical, hydrological and climatological characteristics of a given basin. The research focused on the development of methods for selecting the optimal model structure and parameters by analysing the results obtained for different model structures. This is achieved through the computational environment, in which it is possible to implement different types of hydrological rainfall-runoff models. these models have a unified system of data input, parameter optimisation rules, and procedures for result generation. The developed elements of the computational environment correspond to generation potential of models with a given structure and complexity. Furthermore, within the framework of hyDrO-Path the following components were developed: an application programming interface (aPi), a data assimilation module, a module for computational representation of a real object, and a module for the estimation and optimisation of model parameters. the developed computational environment was applied to prepare a version of tOPO-Flex and perform hydrological validation of the model's results. the hydrological validation was performed for selected flood events in the Bystrzyca Dusznicka subbasin of the nysa kłodzka river.
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