Characterization of Tubular Surfaces in Terms of Finite III-type

d9bb2551-800f-431b-8f93-ba957be9eaf420240405091852984wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL2224-28561991-876310.37394/23203http://wseas.org/wseas/cms.action?id=4073117202411720241910.37394/23203.2024.19https://wseas.com/journals/sac/2024.phpCharacterization of Tubular Surfaces in Terms of Finite III-typeHassanAl-ZoubiDepartment of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, JORDANHamzaAlzaareerDepartment of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, JORDANMohammadAl-RawajbehDepartment of Computer Science, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, JORDANMohammadAl-KafaweenDepartment of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, JORDANIn this paper, we first define relations regarding the first and the second Laplace operators corresponding to the third fundamental form III of a surface in the Euclidean space E 3 . Then, we will characterize the tubular surfaces in terms of their coordinate finite type.45202445202422263https://wseas.com/journals/sac/2024/a065103-001(2024).pdf10.37394/23203.2024.19.3https://wseas.com/journals/sac/2024/a065103-001(2024).pdfB.-Y. Chen, Some open problems and conjectures on submanifolds of finite type, Soochow J. Math, Vol. 17, 1991. J. S. Ro, D. W. Yoon. Tubes of Weingarten types in Euclidean 3-space, J. Cungcheong Math. Soc. Vol. 22 (2009), 359-366. H. Alzaareer, H. Al-Zoubi, F. Abed Al-Fattah, Quadrics with finite Chen-type Gauss map, Journal of Prime Research in Mathematics, Vol.18 No. 1, 2022, 96-107. B.-Y. Chen, F. Dillen, Quadrics, of finite type, J. Geom. Vol. 38, 1990, 16-22. D.-S. Kim, On the Gauss map of quadric hypersurfaces, J. Korean Math. Soc. 31 (1994), 429–437. 10.14712/1213-7243.2020.018B. Senousi, H. Al-Zoubi, Translation surfaces of finite type in Sol3, Commentationes Mathematicae Universitatis Carolinae, Vol. 22, No. 2, 2020, pp 237–256. 10.1007/s00022-012-0136-0M. Bekkar and B. Senoussi, Translation surfaces in the 3-dimensional space satisfying △ III ri= λ i ri, J. Geom., 103 (2012), 367-374. 10.21099/tkbjm/1496162870S. M. Choi, On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space, Tsukuba J. Math. Vol.19 (1995), 285–304. 10.1017/s0004972700028616B.-Y. Chen, F. Dillen, L. Verstraelen, L. Vrancken, Ruled surfaces of finite type, Bull. Austral. Math. Soc. 42, 447-553 (1990). 10.3836/tjm/1270128488Ch. Baikoussis, B.-Y. Chen, L. Verstraelen, Ruled Surfaces and tubes with finite type Gauss map, Tokyo J. Math. Vol. 16 (1993), 341-349. 10.4134/bkms.2009.46.6.1141Y. H. Kim, C. W. Lee, and D. W. Yoon, On the Gauss map of surfaces of revolution without parabolic points, Bull. Korean Math. Soc. Vol. 46 (2009), 1141–1149. 10.1007/s40840-015-0234-xD.-S. Kim, J. R. Kim, Y. H. Kim, Cheng-Yau operator and Gauss map of surfaces of revolution, Bull. Malays. Math. Sci. Soc. 34 (2016), 1319–1327. F. Dillen, J. Pass, L. Verstraelen, On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica Vol. 18, 1990, 239- 246. 10.2996/kmj/1138038815O. Garay, On a certain class of finite type surfaces of revolution, Kodai Math. J. Vol. 11, 1988, 25-31. 10.11650/twjm/1500405286U.-H. Ki, D.-S. Kim, Y. H. Kim, Y.-M. Roh, Surfaces of revolution with pointwise 1-type Gauss map in Minkowski 3-space, Taiwanese J. Math. 13 (2009), 317–338. 10.1007/bf03322254Ch. Baikoussis, L. Verstraelen, The Chentype of the spiral surfaces, Results. Math. Vol. 28, 1995, 214-223. 10.1017/s001708950003055xF. Denever, R. Deszcz, L. Verstraelen, The Chen type of the noncompact cyclides of Dupin, Glasg. Math. J. 36, 1994, 71-75. 10.1007/bf01230997F. Denever, R. Deszcz, L. Verstraelen, The compact cyclides of Dupin and a conjecture by B.-Y Chen, J. Geom. Vol. 46, 1993, 33-38. Ch. Baikoussis, L. Verstraelen, On the Gauss map of helicoidal surfaces, Rend. Semi. Mat. Messina Ser II Vol. 16, 1993, 31-42. B. Senoussi and M. Bekkar, Helicoidal surfaces with △ J r = Ar in 3-dimensional Euclidean space, Stud. Univ. Babes-Bolyai Math. 60 2015, pp 437-448. B.-Y. Chen, Total mean curvature and submanifolds of finite type, World Scientific, Singapore, 1984.