Metrics and norms in non-Euclidean spaces – MiNoNePro

Metrics and norms in non-Euclidean spaces – MiNoNePro

https://www.croris.hr/projekti/projekt/16352

Funding source: European Union
Duration: 1.10.2025 – 30.9.2029
Project Leader: Full Prof. Ema Jurkin, PhD
Budget: 37.169,92 EUR
Call for project proposals: Poziv za financiranje institucionalnih istraživačkih projekata financiran iz izvora 581 – Mehanizam za oporavak i otpornost (2025.) 

Project summary

Within the project, geometric figures, curves, and surfaces are studied in various projective-metric planes and non-Euclidean spaces. Depending on the problem under consideration, methods of synthetic, analytic, and differential geometry, as well as functional analysis, are employed. In projective-metric planes, the emphasis is placed on triangles and quadrilaterals, as well as on the loci of their special points. The properties of certain well-known transformations and their connections with the aforementioned figures are investigated; moreover, some new transformations are defined, and their properties are studied, along with the properties of more complex curves that arise as images of simpler ones. For each resulting curve, its degree and type of circularity are determined. All obtained results are compared with their analogues in the Euclidean plane, whenever such analogues exist. In four-dimensional Lorentz–Minkowski space, the properties of curves in the lightlike plane are studied, as well as involutes and evolutes of curves that have no analogues in Euclidean space. One of the most important types of orthogonality in normed spaces, the so-called Birkhoff–James orthogonality, was the subject of our previous research. We further investigate the structure of this type of orthogonality in Hilbert C*-modules. We also study some other types of orthogonality, such as Roberts orthogonality.

Project Goals

C1: To describe the properties of certain figures and the associated geometric loci of points in projective-metric planes, and, by defining and applying geometric transformations to known curves, to obtain new, more complex curves. To classify all obtained curves with respect to their degree and type of circularity.

C2: To investigate, in four-dimensional Lorentz–Minkowski space, the properties of involutes and evolutes of spatial curves with lightlike normal and binormal vectors, and to study the properties of curves lying on various surfaces, namely the lightlike plane, sphere, horosphere, and equidistant surface.

C3: To investigate the structure of Birkhoff–James orthogonality and Roberts orthogonality in Hilbert C*-modules.

Team members

Members from faculty:
	Full Prof.  Ema Jurkin, - project leader University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Croatia homepage		Full Prof.  Rajna Rajić, PhD University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Croatia homepage
	Assist. Prof. Ivana Filipan, PhD University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Croatia homepage		Nikolina Kovačević, senior lecturer University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Croatia homepage
	Zrinka Vidović-Tisanić, senior lecturer University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Croatia homepage		Toni Čvrljak, assistant University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Croatia homepage
External collaborators:
	Full Prof.  Željka Milin Šipuš, PhD University of Zagreb, Faculty of Science, Croatia homepage		Assist. Prof. Marija Šimić Horvath, PhD University of Zagreb, Faculty of Arhitecture, Croatia homepage
	Assist. Prof. Ljiljana Primorac Gajčić, PhD Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Croatia homepage

Conferences

Published papers