Ljiljana Primorac Gajčić

 

Senior Assistant
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸
phone: +385-31-224-819
fax: +385-31-224-801
email:  lprimora @ mathos.hr
office:  15 (first floor)

 


Research Interests

Pseudo-Riemannian Geometry
Differential Geometry

Degrees

PhD in theoretical mathematics, Department of Mathematics, University of Zagreb , 2016.
BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2007.
 

Publications

 
Journal Publications

  1. 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 (2020), prihvaćen za objavljivanje
  2. 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)
  3. Ž. Milin-Šipuš, Lj. Primorac Gajčić, Minding isometries of ruled surfaces in Lorentz-Minkowski space, Rad HAZU, Matematičke znanosti. 23 (2019), 107-122
  4. 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
    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.


Refereed Proceedings

  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
    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


Others

  1. Lj. Primorac Gajčić, A. Corn, Pravilni zvjezdasti mnogokuti, Osječki matematički list 17/2 (2018), 161-170
  2. Lj. Primorac Gajčić, Al-Khwarizmijeva metoda rješavanja kvadratnih jednadžbi, Matematika i škola 27/83 (2016), 122-124



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Teaching

Zimski semestar:

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Konzultacije (Office Hours): Četvrtkom(Thu) u 11h ili po dogovoru.

 


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