Weingarten and Linear Weingarten Canal Surfaces
In this study, we investigated the (K,H), (K,K_{II}), (H,K_{II})-Weingarten and (K,H),(K,K_{II}),(H,K_{II}) and (K,H,K_{II})-linear Weingarten canal surfaces in IR^3.
math.DG↗
arXiv subjects
Yılmaz Tunçer
Publications and source records attributed to Yılmaz Tunçer.
On geometry of the first and second fundamental forms of canal surfaces
In this study, we analyze the general canal surfaces in terms of the features flat, II-flat minimality and II-minimality, namely we study under which conditions the first and second Gauss and mean curvature vanishes, i.e. K=0, H=0, K_{II}=0 and H_{II} =0. We give a non-existence result for general canal surfaces in E^3 with vanishing the curvatures K, H, K_{II} and H_{II} except the cylinder and cone.We classify the general canal surfaces for which are degenerate according to their radiuses. Finally we obtain that there are no flat, minimal, II-flat and II-minimal general canal surfaces in the Euclidean 3-space such that the center curve has non-zero curvatures.
math.DG↗
Non-Null Weakened Mannheim curves
In this study, non-null Frenet-Mannheim curves and non-null Weakened Mannheim curves are investigated in Minkowski 3-space. Some characterizations for this curves are obtained.
math.DG↗
Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space
In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices.
math.DG↗
New Representations of Bertrand Pairs in Euclidean 3-Space
In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indicatrices made new curve pairs in the means of Mannheim, involte-evolute and Bertrand pairs. Further more, we investigated the relations between the spherical images and introduced new representations of spherical indicatrices.
math.DG↗
Smarandache Curves According to Bishop Frame in Euclidean 3-Space
In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some differential geometric properties of Smarandache curves. Also we find the centers of the osculating spheres and curvature spheres of Smarandache curves.
math.GM↗