Yarı-Galileo Uzayında Belli Bir Ortalama Eğriliğe Sahip Yüzeyler Üzerine

Yıl 2021, Cilt: 11 Sayı: 2, 215 - 226, 31.12.2021

Muhittin Evren Aydın Alper Osman Öğrenmiş

https://doi.org/10.37094/adyujsci.907765

Öz

Bu çalışmada; yarı-Galileo uzayında, öteleme ve ayrışabilir yüzeyler denilen iki belirgin sınıf ele alınmıştır. 𝑣 , bir 𝑣 izotropik vektörün normal bileşeni olmak üzere bu yüzeylerden
ortalama eğriliği 𝐻 = 𝑣! denklemini sağlayanlar elde edilmiştir.

On Surfaces in pseudo-Galilean space with prescribed mean curvature

Öz

In this work, we consider certain classes of surfaces in the pseudo-Galilean space, the translation and factorable surfaces. We classify these surfaces that satisfy the equation H=v^ , where H is the mean curvature and v^ the normal component of an isotropic vector v.

Anahtar Kelimeler

Translating soliton, Manifolds with density, Mean curvature, Pseudo-Galilean space

Kaynakça

• [1] Bueno, A., Translating solitons of the mean curvature flow in the space H^2×R, Journal of Geometry, (109, Article number )42, 2018. https://doi.org/10.1007/s00022-018-0447-x, 2018.
• [2] López, R., Separation of variables in equations of mean-curvature type, Proceedings of the Royal Society of Edinburgh Section A, (146)5146(5), 1017-1035, 2016.
• [3] López, R., Some geometric properties of translating solitons in Euclidean space, Journal of Geometry, (109, Article number )40, 2018. https://doi.org/10.1007/s00022-018-0444-0
• [4] Aydin, M.E., López, R., Ruled translating solitons in Minkowski 3-space, preprintarXiv:2109.05254v1, 2021.
• [5] Aydin, M.E., López, R., Translating solitons by separation of variables, arXiv:2109.05253v1 preprint, 2021.
• [6] Angenent, S., On the formation of singularities in the curve shortening flow, Journal of Differential Geometry, 33, 601-633, 1991.
• [7] Halldorsson, H., Self-similar solutions to the curve shortening flow, Transactions of the American Mathematical Society, (364)10364(10), 5285-5309, 2012.
• [8] Castro, I., Castro-Infantes, I., Castro-Infantes, J., Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers, Open Mathematics, 16,747-766, 2018.
• [9] Altiin, M., Kazan, A., Karadag, H. B., Ruled surfaces in E^3 with density, Honam Mathematical Journal,. 41(4), 683-695, 2019.
• [10] Hieu, D.T., Hoang, N.M., Ruled minimal surfaces in R^3 with density e^z , Pacific Journal of Mathematics, (243)2243(2), 277-285, 2009.
• [11] Abdel-Aziz, H.S., Saad, M.K., Ali, H.A., Affine factorable surfaces in pseudo-Galilean space, arXiv:1812.00765v1 [math.GM].
• [12] Aydin, M. E., , Ogrenmis, A.O., Ergut, M., Classification of factorable surfaces in the pseudo-Galilean space, Glasnik Matematicki Series III, (70)5050(70), 441-451, 2015.
• [13] Aydin, M. E., Kulahci, M. A., Ogrenmis, A.O., Non-zero constant curvature factorable surfaces in pseudo-Galilean space, Communications of the Korean Mathematical Society, 33 (1), 247-259, 2018.
• [14] Aydin, M. E., Kulahci, M. A., Ogrenmis, A.O., Constant curvature translation surfaces in Galilean 3-space, International Electronic Journal of Geometry, 12(1), 9-19, 2019.
• [15] Dede, M., Ekici, C., On minimal surfaces in Galilean space, Conference Proceedings of Science and Technology, (2)22(2), 142-147, 2019.
• [16] Kelleci, A., , Translation-factorable surfaces with vanishing curvatures in Galilean 3-spaces, International Journal of Maps in Mathematics, (4)14(1), 14-26, 2021.
• [17] Milin-Sipus, Z., Divjak, B., Translation surface in the Galilean space, Glasnik Matematicki Series III, (46)246(66), 455-469, 2011.
• [18] Milin-Sipus, Z., On a certain class of translation surfaces in a pseudo-Galilean space, International Mathematical Forum, , (6)236(23), 1113-1125, 2012.
• [19] Yoon, D.W., , Some classification of translation surfaces in Galilean 3-space, International Journal of Mathematical Analysis, (6)2828(6), 1355-1361, 2012.
• [20] Abdel-Baky, R.A., and Unluturk, Y., A study on classification of translation surfaces in pseudo-Galilean 3-space, Journal of Coupled Systems and Multiscale Dynamics, (6)3, 233-240, 2018.
• [21] Bansal, P., , Shahid, M. H., On classification of factorable surfaces in Galilean space G^3, Jordan Journal of Mathematics and Statistics, (12)312(3), 289-306, 2019.
• [22] Cakmak, A., Karacan, M.K., Kiziltug, S., Yoon, D.W., Corrigendum to translation surfaces in the 3-dimensional Galilean space satisfying Δ^II x_i=λ_i x_i , Bulletin of the Korean Mathematical Society, (56)256(2), 549-554, 2019. [23] Lone, M.S., Homothetical surfaces in three dimensional pseudo-Galilean spaces satisfying Δ^II x_i=λ_i x_i, Advances in Applied Clifford Algebras, 29(5), (29)92, 2019. https://doi.org/10.1007/s00006-019-1007-7 [24] Kazan, A., Karadag, H.B., Weighted minimal and weighted flat surfaces of revolution in Galilean 3-space with density, International Journal of Analysis and Applications, (16)316(3), 414-426, 2018. [25] Mosa, S., Elzawy, M., Helicoidal surfaces in Galilean space with density, Frontiers in Physics, 8, Article (8)81, 2020. https://doi.org/10.3389/fphy.2020.00081.
• [26] Yoon, D.W., Weighted minimal translation surfaces in the Galilean space with density, Open Mathematics, 15, 459-466, 2017.
• [27] Yoon, D.W., Lee, J.W., , Lee, C.W., φ- minimal rotational surfaces in pseudo-Galilean space with density, Annales Polonici Mathematici, 120, 183-196, 2017.
• [28] Altin, M., Unal, I., Surface family with common line of curvature in 3-dimensional Galilean space, The journal Facta Universitatis: Series Mathematics and Informatics, (35)535(5), 1315-1325, 2020.
• [29] Divjak, B., Curves in pseudo-Galilean geometry, Annales Universitas Scientiarium Budapestinesis, 41,117-128,1998.
• [30] Milin-Sipus, Z., Divjak, B., Surfaces of constant curvature in the pseudo-Galilean space, International Journal of Mathematics and Mathematical Sciences, Art ID375264, 28pp., 2012.
• [31] Mólnar, E., , The projective interpretation of the eight 3-dimensional homogeneous geometries, Beiträge zur Algebra und Geometrie, (38)238(2), 261-288, 1997.
• [32] Onishchick, A., Sulanke, R., Projective and Cayley-Klein Geometries, Springer, 2006.
• [33] Röschel, O., Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben, 1984.
• [34] López, R., Differential geometry of curves and surfaces in Lorentz-Minkowski space, International Electronic Journal of Geometry, (7)17(1), 44-107, 2014.
• [35] O'Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.