A New Characterization of Tzitzeica Curves in Euclidean 4-Space
Year 2023,
Volume: 4 Issue: 2, 77 - 86, 31.07.2023
Emrah Tunç
,
Bengü Bayram
Abstract
In this study, we are interested in Tzitzeica curves (Tz-curves) in Euclidean 4 -space. Tz-curve condition for Euclidean 4 -space are determined as three types for three hyperplanes and some examples are given.
References
- Bobe A., Boskoff W.G., Ciuca M.G., Tzitzeica type centro-affine invariants in Minkowski space, Analele Stiintifice ale Universitatii Ovidius Constanta, 20(2), 27-34, 2012.
- Bulca B., A Characterization of Surfaces in E4 , Ph.D., Uludağ University, Bursa, Türkiye, 2012.
- Crasmareanu M., Cylindrical Tzitzeica curves implies forced harmonic oscillators, Balkan Journal of Geometry and Its Applications, 7(1), 37-42, 2002.
- Gray A., Modern Differential Geometry of Curves and Surfaces, CRC Press, 1993.
- Gluck H., Higher curvatures of curves in Euclidean space, The American Mathematical Monthly,
73(7), 243-245, 1966.
- Karacan M.K., Bükcü B., On the hyperbolic cylindrical Tzitzeica curves in Minkowski 3-space, Journal of Balıkesir University Institute of Science and Technology, 10(1), 46-51, 2009.
- Karacan M.K., Bükcü B., On the elliptic cylindrical Tzitzeica curves in Minkowski 3-space, Scientia Magna, 5(3), 44-48, 2009.
- Klein F., Lie S., Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren linearen transformationen in sich übergehen, The American Mathematical Monthly, 4, 50-84, 1871.
- Öztürk G., Arslan K., Hacısalihoğlu H., A characterization of ccr-curves in Rn , Proceedings of the Estonian Academy of Sciences, 57, 217-224, 2008.
- Tunç E., A Characterization of Tzitzeica Curves and Surfaces, Ph.D., Balıkesir University, Balıkesir, Türkiye, 2021.
- Tzitzeica G., Sur une nouvelle classe de surfaces, Comptes Rendus des Seances de l’Academie des Sciences Paris, 144(1), 1257-1259, 1907.
- Tzitzeica G., Sur certaines courbes gauches, Annales scientifiques de l’École normale supérieure, 28(3), 9-32, 1911.
Year 2023,
Volume: 4 Issue: 2, 77 - 86, 31.07.2023
Emrah Tunç
,
Bengü Bayram
References
- Bobe A., Boskoff W.G., Ciuca M.G., Tzitzeica type centro-affine invariants in Minkowski space, Analele Stiintifice ale Universitatii Ovidius Constanta, 20(2), 27-34, 2012.
- Bulca B., A Characterization of Surfaces in E4 , Ph.D., Uludağ University, Bursa, Türkiye, 2012.
- Crasmareanu M., Cylindrical Tzitzeica curves implies forced harmonic oscillators, Balkan Journal of Geometry and Its Applications, 7(1), 37-42, 2002.
- Gray A., Modern Differential Geometry of Curves and Surfaces, CRC Press, 1993.
- Gluck H., Higher curvatures of curves in Euclidean space, The American Mathematical Monthly,
73(7), 243-245, 1966.
- Karacan M.K., Bükcü B., On the hyperbolic cylindrical Tzitzeica curves in Minkowski 3-space, Journal of Balıkesir University Institute of Science and Technology, 10(1), 46-51, 2009.
- Karacan M.K., Bükcü B., On the elliptic cylindrical Tzitzeica curves in Minkowski 3-space, Scientia Magna, 5(3), 44-48, 2009.
- Klein F., Lie S., Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren linearen transformationen in sich übergehen, The American Mathematical Monthly, 4, 50-84, 1871.
- Öztürk G., Arslan K., Hacısalihoğlu H., A characterization of ccr-curves in Rn , Proceedings of the Estonian Academy of Sciences, 57, 217-224, 2008.
- Tunç E., A Characterization of Tzitzeica Curves and Surfaces, Ph.D., Balıkesir University, Balıkesir, Türkiye, 2021.
- Tzitzeica G., Sur une nouvelle classe de surfaces, Comptes Rendus des Seances de l’Academie des Sciences Paris, 144(1), 1257-1259, 1907.
- Tzitzeica G., Sur certaines courbes gauches, Annales scientifiques de l’École normale supérieure, 28(3), 9-32, 1911.