2019 **Abstract:** In this paper, a new modified roller coaster surface according to a modified orthogonal frame is investigated in Euclidean 3-space. In this method, a new modified roller coaster surface is modeled. Both the Gaussian curvature and mean curvature of roller coaster surfaces are investigated. Subsequently, we obtain several characterizations in Euclidean 3-space.

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“…The concept of the associated curve basically reveals the relationship between two curves, which is created with the help of a master curve. the differential geometry of curves and surfaces are reviewed in some aspects [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In addition, it has an important place in the literature in terms of its contribution to the investigation of the behavior of these two curves and the investigation of the surfaces that can be formed with these curves.…”

confidence: 99%

“…The concept of the associated curve basically reveals the relationship between two curves, which is created with the help of a master curve. the differential geometry of curves and surfaces are reviewed in some aspects [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In addition, it has an important place in the literature in terms of its contribution to the investigation of the behavior of these two curves and the investigation of the surfaces that can be formed with these curves.…”

confidence: 99%

“…Baş and Körpınar have introduced the rollar coaster surface for the modified orthogonal frame in the Euclidean 3-space. Additionally, some characteristic features of this surfaces have been obtained and visual applications related to modified orthogonal rollar coaster surface and its parallel surface have been given [14]. Lone et al have defined Mannheim pairs, Frenet-Mannheim curves and weakened Mannheim curves according to modified orthogonal frame in the Euclidean 3-space and obtained some characterizations of these www.josa.ro Mathematics Section curves [15].…”

confidence: 99%

“…Then, the applied geometric properties of curve itself are irrespective of some motions. Also, the differential geometry of curves and surfaces are reviewed in some aspects [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

confidence: 99%