Page 348 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 348
DIFFERENTIAL GEOMETRY: OLD AND NEW (MS-15)
New results in the study of magnetic curves in quasi-Sasakian manifolds
of product type
Ana Irina Nistor, ana.irina.nistor@gmail.com
"Gheorghe Asachi" Technical University of Iasi, Romania
This presentation is based on the joint paper with M.I. Munteanu entitled "Magnetic curves in
quasi-Sasakian manifolds of product type" which was accepted for publication in "New Hori-
zons in Differential Geometry and its Related Fields", Eds. T. Adachi and H. Hashimoto, 2021.
The main result represents a positive answer to sustain our conjecture about the order of a
magnetic curve in a quasi-Sasakian manifold. More precisely, we show that the magnetic curves
in quasi-Sasakian manifolds, obtained as the product of a Sasakian and a Kähler manifold, have
maximum order 5.
Next, we study the magnetic curves in S3 ×S2. First, we find the explicit parametrizations of
such curves. Then, we find a necessary and sufficient condition for a magnetic curve in S3 × S2
to be periodic. Finally, we conclude with some examples of magnetic curves in S3 × S2.
On composition of geodesic and conformal mappings between generalized
Riemannian spaces preserving certain tensors
Miloš Petrovic´, petrovic.milos@ni.ac.rs
University of Niš, Serbia
Recently, O. Chepurna, V. Kiosak and J. Mikeš studied geodesic and conformal mappings be-
tweeen two Riemannian spaces preserving the Einstein tensor and among other things proved
that in that case Yano’s tensor of concircular curvature is also invariant with respect to these
mappings. On the other hand I. Hinterleitner and J. Mikeš recently investigated composition
of geodesic and conformal mappings between Riemannian spaces that is at the same time har-
monic. In the present paper we connect these results and consider it in the settings of generalized
Riemannian spaces in Eisenhart’s sense.
Null scrolls, B-scrolls and associated evolute sets in Lorentz-Minkowski
3-space
Ljiljana Primorac Gajcˇic´, ljiljana.primorac@mathos.hr
University of Osijek, Croatia
Coauthors: Željka Milin Šipuš, Ivana Protrka
In classical differential geometry in Euclidean space, the Bonnet’s theorem states that there are
two surfaces of constant mean curvature parallel a surface of constant positive Gaussian cur-
vature. These two constant mean curvature surfaces are so-called harmonic evolutes of each
other. In this short presentation, we present results of the analogous investigation in Lorentz-
Minkowski 3-space, however, restricted to the case of surfaces that have no Euclidean coun-
terpart, the quasi-umbilical surfaces, [1]–[4]. These surfaces are characterized by the property
that their shape operator is not diagonalizable, and they can be parametrized as null scrolls or
B-scrolls, [6]. In [5] we have shown that they are the only surfaces whose evolute set degener-
ates to a curve. The curve is of either null or spacelike causal character, and we analyse them
346
New results in the study of magnetic curves in quasi-Sasakian manifolds
of product type
Ana Irina Nistor, ana.irina.nistor@gmail.com
"Gheorghe Asachi" Technical University of Iasi, Romania
This presentation is based on the joint paper with M.I. Munteanu entitled "Magnetic curves in
quasi-Sasakian manifolds of product type" which was accepted for publication in "New Hori-
zons in Differential Geometry and its Related Fields", Eds. T. Adachi and H. Hashimoto, 2021.
The main result represents a positive answer to sustain our conjecture about the order of a
magnetic curve in a quasi-Sasakian manifold. More precisely, we show that the magnetic curves
in quasi-Sasakian manifolds, obtained as the product of a Sasakian and a Kähler manifold, have
maximum order 5.
Next, we study the magnetic curves in S3 ×S2. First, we find the explicit parametrizations of
such curves. Then, we find a necessary and sufficient condition for a magnetic curve in S3 × S2
to be periodic. Finally, we conclude with some examples of magnetic curves in S3 × S2.
On composition of geodesic and conformal mappings between generalized
Riemannian spaces preserving certain tensors
Miloš Petrovic´, petrovic.milos@ni.ac.rs
University of Niš, Serbia
Recently, O. Chepurna, V. Kiosak and J. Mikeš studied geodesic and conformal mappings be-
tweeen two Riemannian spaces preserving the Einstein tensor and among other things proved
that in that case Yano’s tensor of concircular curvature is also invariant with respect to these
mappings. On the other hand I. Hinterleitner and J. Mikeš recently investigated composition
of geodesic and conformal mappings between Riemannian spaces that is at the same time har-
monic. In the present paper we connect these results and consider it in the settings of generalized
Riemannian spaces in Eisenhart’s sense.
Null scrolls, B-scrolls and associated evolute sets in Lorentz-Minkowski
3-space
Ljiljana Primorac Gajcˇic´, ljiljana.primorac@mathos.hr
University of Osijek, Croatia
Coauthors: Željka Milin Šipuš, Ivana Protrka
In classical differential geometry in Euclidean space, the Bonnet’s theorem states that there are
two surfaces of constant mean curvature parallel a surface of constant positive Gaussian cur-
vature. These two constant mean curvature surfaces are so-called harmonic evolutes of each
other. In this short presentation, we present results of the analogous investigation in Lorentz-
Minkowski 3-space, however, restricted to the case of surfaces that have no Euclidean coun-
terpart, the quasi-umbilical surfaces, [1]–[4]. These surfaces are characterized by the property
that their shape operator is not diagonalizable, and they can be parametrized as null scrolls or
B-scrolls, [6]. In [5] we have shown that they are the only surfaces whose evolute set degener-
ates to a curve. The curve is of either null or spacelike causal character, and we analyse them
346
