Research Interests

• Pseudo-Riemannian Geometry
• Differential Geometry

Degrees

• PhD in theoretical mathematics, Department of Mathematics, University of Zagreb , 2016.
  • Mappings of ruled surfaces in Minkowski space (2.08 MB)
• BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2007.

Publications

1. I. Filipan, Ž. Milin-Šipuš, Lj. Primorac Gajčić, Curves in Lightlike Planes in Three-Dimensional Lorentz–Minkowski Space, Mathematics 11/24 (2023)
2. I. Filipan, Ž. Milin-Šipuš, Lj. Primorac Gajčić, Null-translation surfaces with constant curvatures in Lorentz-Minkowski 3-space, Rad HAZU, Matematičke znanosti. 27 (2023), 219-230
3. R. Lopez, Ž. Milin-Šipuš, Lj. Primorac Gajčić, I. Protrka, Involutes of Pseudo-null Curves in Lorentz-Minkowski 3-space, Mathematics 9/11 (2021)
4. R. Lopez, Ž. Milin-Šipuš, Lj. Primorac Gajčić, I. Protrka, Null scrolls with spacelike harmonic evolutes in Lorentz-Minkowski space, Results in Mathematics 76/1 (2021)
5. Ž. Milin-Šipuš, Lj. Primorac Gajčić, I. Protrka, Generalized helices on a lightlike cone in 3-dimensional Lorentz-Minkowski space, KoG (Scientific and Professional Journal of Croatian Society for Geometry and Graphics) 24/24 (2020), 41-46
6. Lj. Primorac Gajčić, Ž. Milin-Šipuš, I. Protrka, Null scrolls with prescribed curvatures in Lorentz-Minkowski 3-space, Analele Stiintifice ale Universitatii Ovidius Constanta Seria Matematica 28/3 (2020), 229-240
7. R. Lopez, Ž. Milin-Šipuš, Lj. Primorac Gajčić, I. Protrka, Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz–Minkowski space, International Journal of Geometric Methods in Modern Physics 16/5 (2019)
8. Ž. Milin-Šipuš, Lj. Primorac Gajčić, Minding isometries of ruled surfaces in Lorentz-Minkowski space, Rad HAZU, Matematičke znanosti. 23 (2019), 107-122
9. Ž. Milin-Šipuš, Lj. Primorac Gajčić, I. Protrka, Null scrolls as B-scrolls in Lorentz-Minkowski 3-space, Turkish Journal of Mathematics 43/6 (2019), 2908-2920
   Abstract

   Null scrolls, i.e. ruled surfaces whose base curve and rulings are both lightlike (null), are Lorentzian surfaces having no Euclidean counterparts. In this work we present reparametrization of nondegenerate null scroll as a B-scroll, i.e. as a ruled surface whose rulings correspond to the binormal vectors of a base curve. We prove that the curvature of a base curve, which determines the Gaussian and mean curvature of a null scroll, is invariant under such a reparametrization. We also determine a one-parameter family of null curves on null scroll which serve as base curves for this kind of reparametrization.

1. Lj. Primorac Gajčić, Ž. Milin-Šipuš, I. Protrka, Structure Functions of Ruled Surfaces with Null Rulings , The 18th International Conference on Geometry and Graphics, Milano, 2018, 371-380
   Abstract

   In this paper we analyze ruled surfaces in Lorentz-Minkowski space in terms of their structure functions. We are especially interested in ruled surfaces which do not have a Euclidean counterpart, that is, surfaces with null rulings, and in particular, so-called B- scrolls. For ruled surfaces in Lorentz- Minkowski space, we establish relations between their structure functions and curvatures. Structure functions can be used for e.g. proving the classical Dini-Beltrami theorem which states (in Euclidean space) that a ruled skew Weingarten surface is a piece of a helicoidal surface. In Lorentz-Minkowski space, the problem is more complex, due to the different types of surfaces with respect to their inherited metrics. It turns out that all null-ruled surfaces are Weingarten, however their structure functions need not be constant. In this paper we analyze helicoidal surfaces among Weingarten null-ruled surfaces in terms of their structure functions.
2. Lj. Primorac Gajčić, On local isometries of B-scrolls in Minkowski space, The Young Researcher Workshop on Differential Geometry in Minkowski Space, Granada, Spain, 2017, 125-132
3. Lj. Primorac Gajčić, Ž. Milin-Šipuš, Ruled Surfaces of Constant Slope in 3-Minkowski Space, 16th International Conference on Geometry and Graphics, Innsbruck, 2014

1. M. Đuzel, I. Filipan, Lj. Primorac Gajčić, Krivulje u trodimenzionalnom Minkowskijevom prostoru, KoG (Scientific and Professional Journal of Croatian Society for Geometry and Graphics) 27 (2023)
2. I. Filipan, E. Jurkin, Ž. Milin-Šipuš, Lj. Primorac Gajčić, Radionica „Plohe od sapunice“, Osječki matematički list 22 (2022)
3. Lj. Primorac Gajčić, Neke manje poznate kružnice u geometriji trokuta, Osječki matematički list 20/2 (2020), 87-97
4. M. Alilović, Z. Kolar-Begović, Lj. Primorac Gajčić, Wallace-Simsonov pravac, Osječki matematički list 19/2 (2019), 137-146
   Abstract

   U radu se razmatra pravac na kojem leže nožišta okomica, povuče- nih na stranice trokuta, iz točke koja leži na kružnici opisanoj tom tro- kutu. Taj pravac je u literaturi poznat pod imenom Wallace-Simsonov pravac. Navedeni su zanimljivi elementi povijesti otkrića ovog pravca. Promatrana su neka njegova zanimljiva geometrijska svojstva te veze s Eulerovom kružnicom trokuta.
5. Lj. Primorac Gajčić, A. Corn, Pravilni zvjezdasti mnogokuti, Osječki matematički list 17/2 (2018), 161-170
6. Lj. Primorac Gajčić, Al-Khwarizmijeva metoda rješavanja kvadratnih jednadžbi, Matematika i škola 27/83 (2016), 122-124

Teaching

Konzultacije (Office Hours): Ponedjeljkom u 12.15h ili po dogovoru.

Prijedlog tema završnih radova (akademska 2024./2025.)

1. Mannheimov par krivulja (odabrana)
2. Fundamentalni teorem ravninskih krivulja (odabrana)
3. Geodetske krivulje (odabrana)
4. Preslikavanja ploha (odabrana)
5. Eulerov poučak (odabrana)

Prijedlog tema diplomskih radova (akademska 2024./2025.)

1. Minimalne plohe (odabrana)
2. Kvaternioni (slobodna)
3. Krivulje u koordinatnom sustavu (odabrana)
4. Plohe u koordinatnom sustavu (slobodna)
5. Poučavanje eksponencijalne i logaritamske funkcije (odabrana)