Time-like Involutes of a space-like helix in Minkowski space-time
نویسندگان
چکیده
In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus of involute and evolute curves by the method expressed as in [11]. Moreover, we also proved that the time-like involute cannot be a helix, a general helix or a type-3 slant helix, respectively.
منابع مشابه
On the Differential Geometry of the Curves in Minkowski Space-Time II
In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated. Keywords—Frenet Apparatus, Time-like Curves, Minkowski Space-time.
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