2012 **Abstract:** 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 representat…

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“…Well-known pairs of curves are Involute-Evolute, Parallel, Bertrand, Mannheim, and Natural mates. Characterizations of these curves mates with some properties can be found in various papers : [2,6,12,13,14,15,20,23,25,27,31,32,39,42]. Some of these curves mates have been generalized to larger dimensions and have been studied by many authors [11,17,19,28,35].…”

confidence: 99%

“…Well-known pairs of curves are Involute-Evolute, Parallel, Bertrand, Mannheim, and Natural mates. Characterizations of these curves mates with some properties can be found in various papers : [2,6,12,13,14,15,20,23,25,27,31,32,39,42]. Some of these curves mates have been generalized to larger dimensions and have been studied by many authors [11,17,19,28,35].…”

confidence: 99%

“…The some relations between slant helices and their involutes, spherical images in three dimensional Lie groups are given in [12]. The some features of the spherical indicatrices of a Bertrand curve and its mate curve are presented in Euclidean 3-space in [13].…”

confidence: 99%