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2016•Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik BilimlerOpen access

HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE

Mehdi Jafarı

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Abstract

A complete treatment of one parameter homothetic motions in three and four dimensional Euclidean spaces is provided in the Yayli's PhD thesis [15].Here we follow his idea to define one parameter homothetic motion in generalized 3-space 3E.  By means of the generalized Hamilton operators, we also define a Hamilton motion and show that it is a homothetic motion.We investigate some properties of this motion and show that Darboux vector of the motion can be written as multiplication of two generalized quaternions.

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A complete treatment of one parameter homothetic motions in three and four dimensional Euclidean spaces is provided in the Yayli's PhD thesis [15].Here we follow his idea to define one parameter homothetic motion in generalized 3-space 3E.  By means of the generalized Hamilton operators, we also define a Hamilton motion and show that it is a homothetic motion.We investigate some properties of this motion and show that Darboux vector of the motion can be written as multiplication of two generalized quaternions.

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Available abstract

A complete treatment of one parameter homothetic motions in three and four dimensional Euclidean spaces is provided in the Yayli's PhD thesis [15].Here we follow his idea to define one parameter homothetic motion in generalized 3-space 3E.  By means of the generalized Hamilton operators, we also define a Hamilton motion and show that it is a homothetic motion.We investigate some properties of this motion and show that Darboux vector of the motion can be written as multiplication of two generalized quaternions.

Key concepts: Homothetic transformation, Motion (physics), Mathematics, Euclidean space, Space (punctuation), Euclidean geometry, Mathematical analysis, Pure mathematics

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