1a5b2e10-a919-46e8-9ae6-fa4a403f2abf20221104093307875wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40511520221520222110.37394/23206.2022.21https://wseas.com/journals/mathematics/2022.phpHassanAl-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, JORDANAmjedZraiqatDepartment of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, JORDANTareqHamadnehDepartment of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, JORDANWaseemAl-MashalehDepartment of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, JORDANThis article. in the introduction, gives a brief historic description on surfaces of finite Chen-type and of coordinate finite Chen-type according to the first, second and third fundamental form of a surface in the Euclidean E^3 space . Then, an important class of surfaces was introduced, namely, the ruled surfaces were classified according to its coordinate finite Chen type with respect to the second fundamental form.1142022114202276576987https://wseas.com/journals/mathematics/2022/b765106-053(2022).pdf10.37394/23206.2022.21.87https://wseas.com/journals/mathematics/2022/b765106-053(2022).pdfH. Al-Zoubi, A. Dababneh, M. Al-Sabbagh, Ruled surfaces of finite II-type, WSEAS Trans. Math. 18 (2019), pp. 1-5.10.1109/icit52682.2021.9491118H. Al-Zoubi, H. Alzaareer, T. Hamadneh, M. Al Rawajbeh, Tubes of coordinate finite type Gauss map in the Euclidean 3-space, Indian J. Math. 62 (2020), 171-182.10.1109/icit52682.2021.9491118H. Al-Zoubi, M. Al-Sabbagh, Anchor rings of finite type Gauss map in the Euclidean 3-space, Int. J. Math. Comput. Methods 5 (2020), 9-13.10.3390/axioms11070326H. Al-Zoubi, A. K. Akbay, T. Hamadneh, and M. Al-Sabbagh, Classification of surfaces of coordinate finite type in the Lorentz-Minkowski 3-space. Axioms 11 (2022).10.1007/bf03322254Ch. Baikoussis, L. Verstraelen, The Chen-type of the spiral surfaces, Results. Math. 28, 214-223 (1995).B.-Y. Chen, Surfaces of finite type in Euclidean 3-space, Bull. Soc. Math. Belg. Ser. B 39 243-254 (1987).B.-Y. Chen, Total mean curvature and submanifolds of finite type, Second edition, World Scientific Publisher, (2014).B.-Y. Chen, Some open problems and conjectures on submanifolds of finite type, Soochow J. Math. 17 (1991), pp. 169-188.B.-Y. Chen, F. Dillen, Quadrics, of finite type, J. Geom. 38, 16-22 (1990).10.1017/s0004972700028616B.-Y. Chen, F. Dillen, L. Verstraelen, L. Vrancken, Ruled surfaces of finite type, Bull. Austral. Math. Soc. 42, 447-553 (1990).10.1007/bf01230997F. Denever, R. Deszcz L. Verstraelen, The compact cyclides of Dupin and a conjecture by B.-Y Chen, J. Geom. 46, 33-38 (1993).10.1017/s001708950003055xF. Denever, R. Deszcz L. Verstraelen, The Chen type of the noncompact cyclides of Dupin, Glasg. Math. J. 36, 71-75 (1994).10.1090/s0002-9939-1988-0929414-2O. Garay, Finite type cones shaped on spherical submanifolds, Proc. Amer. Math. Soc. 104, 868-870 (1988).M. Mhailan, M. Abu Hammad, M. Al Horani, R. Khalil, On fractional vector analysis, J. Math. Comput. Sci. 10 (2020), 2320-2326.10.14712/1213-7243.2020.018B. Senoussi, H. Al-Zoubi, Translation surfaces of finite type in Sol3, Comment. Math. Univ. Carolin. 61 (2020), pp. 237-256.