Evolution of Tzitzeica hypersurfaces

• Main Authors: Constantin Udriste, Ionel Tevy, Ali Sapeeh Rasheed
• Format: Article
• Language: English
• Published: Accademia Peloritana dei Pericolanti 2018-06-01
• Series: Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali
• Online Access: http://dx.doi.org/10.1478/AAPP.961A7

Our aim is to study the evolutions of Tzitzeica hypersurfaces which appear in understanding the dynamics of some geometric programming problems and reliability optimal allocation problems. Section 2 analyses the convexity of a Tzitzeica hypersurface. Sections 3-6 refer to standard Tzitzeica hypersurfaces and their evolutions by convenient geometrical flows: (i) evolution along the normal vector field, (ii) infinitesimal normal transformation of a Tzitzeica hypersurface, (iii) evolution along a centro-affine vector field, and (iv) evolution along an affine vector field. Sections 7-8 include results on the Tzitzeica law in economics and the evolution of Tzitzeica surfaces described by PDEs: (v) Tzitzeica hypersurfaces as invariants w.r.t. excess demand flow; (vi) parametric Tzitzeica surfaces based on PDEs and their evolutions.