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Yarı-Galileo Uzayında Belli Bir Ortalama Eğriliğe Sahip Yüzeyler Üzerine

Year 2021, Volume 11, Issue 2, 215 - 226, 31.12.2021
https://doi.org/10.37094/adyujsci.907765

Abstract

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.

References

  • [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.

On Surfaces in pseudo-Galilean space with prescribed mean curvature

Year 2021, Volume 11, Issue 2, 215 - 226, 31.12.2021
https://doi.org/10.37094/adyujsci.907765

Abstract

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.

References

  • [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.

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Muhittin Evren AYDIN
FIRAT UNIVERSITY
0000-0001-9337-8165
Türkiye


Alper Osman ÖĞRENMİŞ (Primary Author)
Fırat University
0000-0001-5008-2655
Türkiye

Publication Date December 31, 2021
Application Date April 1, 2021
Acceptance Date August 4, 2021
Published in Issue Year 2021, Volume 11, Issue 2

Cite

Bibtex @research article { adyujsci907765, journal = {Adıyaman University Journal of Science}, issn = {2147-1630}, eissn = {2146-586X}, address = {}, publisher = {Adıyaman University}, year = {2021}, volume = {11}, number = {2}, pages = {215 - 226}, doi = {10.37094/adyujsci.907765}, title = {On Surfaces in pseudo-Galilean space with prescribed mean curvature}, key = {cite}, author = {Aydın, Muhittin Evren and Öğrenmiş, Alper Osman} }
APA Aydın, M. E. & Öğrenmiş, A. O. (2021). On Surfaces in pseudo-Galilean space with prescribed mean curvature . Adıyaman University Journal of Science , 11 (2) , 215-226 . DOI: 10.37094/adyujsci.907765
MLA Aydın, M. E. , Öğrenmiş, A. O. "On Surfaces in pseudo-Galilean space with prescribed mean curvature" . Adıyaman University Journal of Science 11 (2021 ): 215-226 <https://dergipark.org.tr/en/pub/adyujsci/issue/67254/907765>
Chicago Aydın, M. E. , Öğrenmiş, A. O. "On Surfaces in pseudo-Galilean space with prescribed mean curvature". Adıyaman University Journal of Science 11 (2021 ): 215-226
RIS TY - JOUR T1 - On Surfaces in pseudo-Galilean space with prescribed mean curvature AU - Muhittin Evren Aydın , Alper Osman Öğrenmiş Y1 - 2021 PY - 2021 N1 - doi: 10.37094/adyujsci.907765 DO - 10.37094/adyujsci.907765 T2 - Adıyaman University Journal of Science JF - Journal JO - JOR SP - 215 EP - 226 VL - 11 IS - 2 SN - 2147-1630-2146-586X M3 - doi: 10.37094/adyujsci.907765 UR - https://doi.org/10.37094/adyujsci.907765 Y2 - 2021 ER -
EndNote %0 Adıyaman University Journal of Science On Surfaces in pseudo-Galilean space with prescribed mean curvature %A Muhittin Evren Aydın , Alper Osman Öğrenmiş %T On Surfaces in pseudo-Galilean space with prescribed mean curvature %D 2021 %J Adıyaman University Journal of Science %P 2147-1630-2146-586X %V 11 %N 2 %R doi: 10.37094/adyujsci.907765 %U 10.37094/adyujsci.907765
ISNAD Aydın, Muhittin Evren , Öğrenmiş, Alper Osman . "On Surfaces in pseudo-Galilean space with prescribed mean curvature". Adıyaman University Journal of Science 11 / 2 (December 2021): 215-226 . https://doi.org/10.37094/adyujsci.907765
AMA Aydın M. E. , Öğrenmiş A. O. On Surfaces in pseudo-Galilean space with prescribed mean curvature. ADYU J SCI. 2021; 11(2): 215-226.
Vancouver Aydın M. E. , Öğrenmiş A. O. On Surfaces in pseudo-Galilean space with prescribed mean curvature. Adıyaman University Journal of Science. 2021; 11(2): 215-226.
IEEE M. E. Aydın and A. O. Öğrenmiş , "On Surfaces in pseudo-Galilean space with prescribed mean curvature", Adıyaman University Journal of Science, vol. 11, no. 2, pp. 215-226, Dec. 2021, doi:10.37094/adyujsci.907765

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