Page 349 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 349
DIFFERENTIAL GEOMETRY: OLD AND NEW (MS-15)
respectively.
References
[1] J. N. Clelland, Totally quasi-umbilical timelike surfaces in R1,2, Asian J. Math, 16(2012),
189-208
[2] K. L. Duggal and A. Bejancu, Lightlike Submanifolds of semi-Riemannian Manifolds and
Applications, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht,
1996.
[3] K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Birkhäuser,
Basel, 2010.
[4] J.-I. Inoguchi and S. Lee, Null curves in Minkowski 3-space, Int. Electron. J.Geom.
1(2008), 40-83.
[5] R. Lopez, Ž. Milin Šipuš, Lj. Primorac Gajcˇic´ and I. Protrka, Harmonic Evolutes of B-
Scrolls with Constant Mean Curvature in Lorentz-Minkowski Space, Int. J. Geom. Meth-
ods Mod. Phys. 2019, https://doi.org/10.1142/S0219887819500762
[6] Ž. Milin Šipuš, Lj. Primorac Gajcˇic´ and I. Protrka, Null scrolls as B-scrolls in Lorentz-
Minkowski Space, Turk J Math, 43(6) (2019): 2908-2920, doi: 10.3906/mat-1904-14.
Non-holonomic equations for sub-Riemannian extremals and metrizable
parabolic geometries
Jan Slovak, slovak@math.muni.cz
Masaryk University, Czech Republic
I will report several recent attempts linking sub-Riemannian geometries to the rich geometry
of filtered manifolds, particularly the parabolic ones. After touching on some relation between
the canonical Cartan geometries, I shall present an approach to sub-Riemannian extremals mo-
tivated by the tractor calculus. Finally, I will explore some implications of the BGG machinery
to the (sub-Riemannian) metrizability of parabolic geometries. All that will be based on joined
work with D. Alekseevsky, A. Medvedev, R. Gover, D. Calderbank, V. Soucek.
Simple closed geodesics on regular tetrahedra in spaces of constant
curvature
Darya Sukhorebska, suhdaria0109@gmail.com
B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of
Sciences of Ukraine (B. Verkin ILTPE of NASU), Ukraine
Coauthor: Alexander Borisenko
Since regular triangles form a regular tiling of Euclidean plane it easily follows the full classi-
fication of closed geodesics on a regular tetrahedron in Euclidean space.
347
respectively.
References
[1] J. N. Clelland, Totally quasi-umbilical timelike surfaces in R1,2, Asian J. Math, 16(2012),
189-208
[2] K. L. Duggal and A. Bejancu, Lightlike Submanifolds of semi-Riemannian Manifolds and
Applications, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht,
1996.
[3] K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Birkhäuser,
Basel, 2010.
[4] J.-I. Inoguchi and S. Lee, Null curves in Minkowski 3-space, Int. Electron. J.Geom.
1(2008), 40-83.
[5] R. Lopez, Ž. Milin Šipuš, Lj. Primorac Gajcˇic´ and I. Protrka, Harmonic Evolutes of B-
Scrolls with Constant Mean Curvature in Lorentz-Minkowski Space, Int. J. Geom. Meth-
ods Mod. Phys. 2019, https://doi.org/10.1142/S0219887819500762
[6] Ž. Milin Šipuš, Lj. Primorac Gajcˇic´ and I. Protrka, Null scrolls as B-scrolls in Lorentz-
Minkowski Space, Turk J Math, 43(6) (2019): 2908-2920, doi: 10.3906/mat-1904-14.
Non-holonomic equations for sub-Riemannian extremals and metrizable
parabolic geometries
Jan Slovak, slovak@math.muni.cz
Masaryk University, Czech Republic
I will report several recent attempts linking sub-Riemannian geometries to the rich geometry
of filtered manifolds, particularly the parabolic ones. After touching on some relation between
the canonical Cartan geometries, I shall present an approach to sub-Riemannian extremals mo-
tivated by the tractor calculus. Finally, I will explore some implications of the BGG machinery
to the (sub-Riemannian) metrizability of parabolic geometries. All that will be based on joined
work with D. Alekseevsky, A. Medvedev, R. Gover, D. Calderbank, V. Soucek.
Simple closed geodesics on regular tetrahedra in spaces of constant
curvature
Darya Sukhorebska, suhdaria0109@gmail.com
B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of
Sciences of Ukraine (B. Verkin ILTPE of NASU), Ukraine
Coauthor: Alexander Borisenko
Since regular triangles form a regular tiling of Euclidean plane it easily follows the full classi-
fication of closed geodesics on a regular tetrahedron in Euclidean space.
347
