Mića S. Stanković

Special equitorsion almost geodesic mappings of the third type of non-symmetric affine connection spaces

Abstract In this paper we investigate a special kind of almost geodesic mapping of the third type of spaces with non-symmetric affine connection. Also we find some relations for curvature tensors of associated affine connection spaces of almost geodesic mappings of the third type. Finally, we investigate equitorsion almost geodesic mapping having the property of reciprocity and find an invariant geometric object of this mapping.

On geodesic mappings of equidistant generalized Riemannian spaces

Abstract In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented.

On Equitorsion Geodesic Mappings of General Affine Connection Spaces

In the papers [19], [20] several Ricci type identities are obtained by using non-symmetric affine connection. In these identities appear 12 curvature tensors, 5 of which being independent [21], while the rest can be expressed as linear combinations of the others. In the general case of a geodesic mapping f of two non-symmetric affine connection spaces GAN and GAN it is impossible to obtain a generalization of the Weyl projective curvature tensor. In the present paper we study the case when GAN and GAN have the same torsion in corresponding points. Such a mapping we name ”equitorsion mapping”. With respect to each of mentioned above curvature tensors we have obtained quantities E θ i jmn (θ = 1, · · · , 5), that are generalizations of the Weyl tensor, i.e. they are invariants based on f . Among E θ only E 5 is a tensor. All these quantities are interesting in constructions of new mathematical and physical structures. AMS Subj. Class.: 53B05.

MINIMAL SURFACES FOR ARCHITECTURAL CONSTRUCTIONS

Minimal surfaces are the surfaces of the smallest area spanned by a given boundary. The equivalent is the definition that it is the surface of vanishing mean curvature. Minimal surface theory is rapidly developed at recent time. Many new examples are constructed and old altered. Minimal area property makes this surface suitable for application in architecture. The main reasons for application are: weight and amount of material are reduced on minimum. Famous architects like Otto Frei created this new trend in architecture. In recent years it becomes possible to enlarge the family of minimal surfaces by constructing new surfaces.