Abstract
In this paper, the position vector equation of   the Frenet curves with constant curvatures in Minkowski 4 -space has been presented. New types for retractions and deformation retracts of Frenet curves in  are deduced. The relations between the Frenet apparatus of the Frenet curves before and after the deformation retracts are obtained.
Highlights
Introduction and DefinitionsMinkowski space time in is an Euclidean space provided with the standard flat metric given by 〈, 〉 = − + + +, where (, ) and (, ) are rectangular coordinate system in
We introduce some characterizations of retraction and deformation retract of Frenet curves in by the components of the position vector according to the Frenet equations
We introduce types of retraction on Frenet curves with non-zero curvature in
Summary
. Since 〈 , 〉 is an indefinite metric, recall that a vector ∈ can have one of the three casual characters; it can be space like, if < , > > 0 or = 0, time like, if < , > < 0, null or light like if < , > = 0 and ≠ 0. Space like or time-like curve ( ) is said to be parametrized by arclength function s, if ( ( ), ( )) = ±1. Are said to be orthogonal vectors if ( , ) = 0 We introduce some characterizations of retraction and deformation retract of Frenet curves in by the components of the position vector according to the Frenet equations. We obtain some relations among curvatures of Frenet curves and their deformation retracts
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