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Abstract:
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The field of research in this dissertation is consideration of different types of curves in Minkowski spaces, as well as defining the notion of hyperbolic angle between spacelike and timelike vector.
The research in this dissertation is connected with the following subjects: geometry of hyperquadrics in Minkowski space, finite type submanifolds and plane Minkowski geometry.
This dissertation, beside Preface and References with 56 items, consists of four chapters: 1. Curves in hyperquadrics in Minkowski spaces; 2. Classification of 2 –type curves in Minkowski n-space ; 3. W-curves in Minkowski space-time; 4. Hyperbolic angle between vectors.
In Chapter 1 the curves lying in hyperquadrics in Minkovski 3-space and Minkowski 4-space are studied. More precisely, the results related with the spacelike and timelike curves lying pseudosphere in Minkowski 3-space are presented. Also, the necessary and sufficient conditions for spacelike curves lying in pseudohyperbolic space in Minkowski 4-space are given.
Curves of finite type 2 in Minkowski n-space are studied in details in Chapter 2. Also, there are given some known results related with finite type submanifolds.
In Chapter 3, W-curves (i.e. the curves having constant all curvature functions) in Minkowski space-time are studied and some relations between W-curves and finite type curves are given.
Finally, in Chapter 4 one of the basic notions in Lorentzian geometry is considered, i.e. hyperbolic angle between two non-null vectors. The notion of hyperbolic angle between two timelike vectors is well-known, so in this chapter it is defined the notion between spacelike and timelike vectors. The measure of hyperbolic angle is also defined. By using the notion of hyperbolic angle between spacelike and timelike vectors, all spacelike curves of constant precession with non-null principal normal and all timelike curves of constant precession in Minkowski 3-space are classified and their explicit parameter equations are given. |