HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE

Year 2016, Volume: 4 Issue: 1, 43 - 51, 12.03.2016

Mehdi Jafari

https://doi.org/10.20290/btdb.15221

Abstract

A complete treatment of one parameter homothetic motions in three and four dimensional Euclidean spaces is provided in the Yayli's PhD thesis (Yaylı, 1988). Here we follow his idea to define one parameter homothetic motion in generalized 3-space  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.  

HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE

Abstract

Üç ve dört boyutlu Öklid uzayinda, bir parametre homotetik hareketleri Yaylı’nın doktora tezin’de [15] tam olarak temın edilir. Burada biz bu fikri kulanarak, genelleştirilmiş 3-boyutlu uzayda bir parametre homotetik hareketi tanıtırdık. Genelleştirilmiş Hamilton operatörler ile, aynı zamanda Hamilton hareket tanımlar ve bu bir homototik hareket olduğunu göstermektedir.Bu hareketın bazı özelliklerini araştırdık ve gösterdik ki bu hareketin Darboux vektörü İki genelleştirilmiş kuaterniyonların çarpmasi yazilabilir

Keywords

Darboux vektör, Genelleştirilmiş Hamilton operatör, Genelleştirilmiş kuaterniyon, homotetik hareket, Pol noktası

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