caa a22 4500 378866591 CHVBK 20180305123359.0 cr unu---uuuuu 161128e20030901xx s 000 0 eng 10.1515/156939403769237033 doi (NATIONALLICENCE)gruyter-10.1515/156939403769237033 On the explicit characterization of spherical curves in n-dimensional Euclidean space [Elektronische Daten] [H. Kocayigit, N. Yaz, C. Camci, H. H. Hacisalihoglu] It is known that a curve in 3-dimensional Euclidean space is spherical if and only if where k 1 and k 2 are its first curvature function and second curvature function, respectively. In 1971, integral form of (1) was given [2] as In the present work, a) it is given another method for (2); b) it is shown that the differential equation characterizing a spherical curve in n-dimensional Euclidean space n ≥ 3 can be solved explicitly to express nth curvature function of the curve in terms of its curvatures and its other curvature functions; c) it is shown that integral form of the generalization of (1) gives us (2) as a spherical case for n = 3. Copyright 2003, Walter de Gruyter Kocayigit H. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut Yaz N. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut Camci C. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut Hacisalihoglu H. H. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 245-254 0928-0219 11:3<245 2003 11 jiip https://doi.org/10.1515/156939403769237033 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403769237033 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kocayigit H. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut NATIONALLICENCE 700 1- Yaz N. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut NATIONALLICENCE 700 1- Camci C. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut NATIONALLICENCE 700 1- Hacisalihoglu H. H. Ankara University, Faculty of Science, Department of Mathematics, 06100, Tandogan, Ankara, Turkey. E-mail: Hacisali@science.ankara.edu.tr aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 245-254 0928-0219 11:3<245 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter