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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space $\mathbf{E}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature $K$ if and only if the surface is flat, i.e. $K=0$.
(2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.
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참고문헌 (10)
참고문헌 신청
Ali A.T. / 2010 / Position vectors of general helices in Euclidean 3-space / Bull. Math. Anal. Appl 3 (2) : 198 ~ 205
Ali A.T. / 2012 / Position vectors of slant helices in Euclidean 3-space / J. Egyptian Math. Soc 20 (1) : 1 ~ 6
Delaunay C. / 1841 / Sur la surface de r evolution dont la courbure moyenne est constante / J. Math. Pure Appl 6 : 309 ~ 320
Enneper A. / 1866 / Ueber die cyclischen Flachen, Nach. K onigl. Ges. d. Wisseensch. G ottingen / Math. Phys : 243 ~ 249
Enneper A. / 1869 / Die cyclischen Flachen / Z. Math. Phys 14 : 393 ~ 421
Ali A.T. / 2012 / Position vectors of slant helices in Euclidean 3-space / J. Egyptian Math. Soc 20 (1) : 1 ~ 6
Delaunay C. / 1841 / Sur la surface de r evolution dont la courbure moyenne est constante / J. Math. Pure Appl 6 : 309 ~ 320
Enneper A. / 1866 / Ueber die cyclischen Flachen, Nach. K onigl. Ges. d. Wisseensch. G ottingen / Math. Phys : 243 ~ 249
Enneper A. / 1869 / Die cyclischen Flachen / Z. Math. Phys 14 : 393 ~ 421
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