Gradient-type deformations of cycles in EPH geometries
DOI:
https://doi.org/10.24193/subbmath.2020.4.10Keywords:
EPH geometries, cycle, deformation, orthogonality, rotation.Abstract
The aim of this paper is to study the cycles of EPH geometries through their homogeneous gradient-type deformations recently introduced by the author. A special topic is the orthogonality between a given cycle C and its deformations as well as between C and its rotated version R(C).
Mathematics Subject Classification (2010): 51N25, 51M09, 53A40.
References
Chuaqui, M., Duren, P., Osgood, B., Ellipses, near ellipses, and harmonic M¨obius transformations, Proc. Am. Math. Soc., 133(2005), no. 9, 2705-2710.
Crasmareanu, M., A gradient-type deformation of conics and a class of Finslerian flows, An. S¸tiin¸t. Univ. Ovidius Constan¸ta, Ser. Mat., 25(2017), no. 2, 85-99.
Crasmareanu, M., A complex approach to the gradient-type deformations of conics, Bull. Transilv. Univ. Bra¸sov, Ser. III, Math. Inform. Phys., 10(59)(2017), no. 2, 59-62.
Crasmareanu, M., From rotation of conics to a class of Finslerian flows, Annals Univ. Craiova Ser. Mat. Inf., 45(2018), no. 2, 275-282.
Crasmareanu, M., A mixed gradient-type deformation of conics and a class of Finslerian- Riemannian flows, An. Univ. Oradea Fasc. Mat., 26(2019), no. 1, 101-107.
Kisil, V.V., Starting with the group SL2(R), Notices Am. Math. Soc., 54(2007), no. 11, 1458-1465.
Kisil, V.V., Geometry of M¨obius Transformations. Elliptic, Parabolic and Hyperbolic Actions of SL2(R), Hackensack, NJ: World Scientific, 2012.
Rovenski, V., Modeling of Curves and Surfaces with MATLAB, Springer Undergraduate Texts in Mathematics and Technology, Springer Berlin, 2010.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.