An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(TpM) for all p ∈ M , which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i. e. S = HId (and thus S is trivially preserved). First we solve an algebraic problem. We determine the n...

In [1] the pseudo-metric dist min on compact subsets A and B of a topological space generated from arbitrary metric space is defined. Using this notion we define the Hausdorff distance (see e.g. [5]) of A and B as a maximum of the two pseudo-distances: from A to B and from B to A. We justify its distance properties. At the end we define some special notions which enable to apply the Hausdorff d...

I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat metric. This generalizes the usual embedding widely used for the de Sitter models. I give the coordinate transformations for the embedding. Taking into account th...

In this paper we study multidimensional persistence modules [5, 13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the category of tame functors. We show how this pseudo-metric can be used to identify persistent features of compact mul-tidimensional persistence modules. To count such features we introduce the feature counting invariant and ...

We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two dimensions are intimately related to the minimal surfaces in a flat pseudo Riemannian 3-space. We define two dimensional surfaces conformally related to the minimal s...

In [2] the pseudo-metric distmax min on compact subsets A and B of a topological space generated from arbitrary metric space is defined. Using this notion we define the Hausdorff distance (see e.g. [6]) of A and B as a maximum of the two pseudo-distances: from A to B and from B to A. We justify its distance properties. At the end we define some special notions which enable to apply the Hausdorf...