Focal curves and focal surfaces in finite dimensional minkowski space

In this thesis, focal curves and focal surfaces in the finite dimensional Minkowski spaces are handled. The geometric properties of focal curves and focal curvatures of a non-null regular curve are examined and by means of the Darboux frame of a non-null curve on the spacelike and timelike surface, its pseudo-spherical evolutes are investigated. Then, in terms of the singularity theory, the focal surfaces of mixed surfaces whose one part is spacelike and the other part is timelike are analyzed by defining as the bifurcation set of the family of distance squared function. Besides, the evolutes of hypersurfaces in hiperbolic m-space are presented and the contact of hypersurfaces with hyperspheres or equidistant hyperplanes are studied via these evolutes. The focal surfaces generated by normal line congruences, which has not been done before, are described in the Minkowski 3-space and their geometry is studied. Moreover, by defining some important curves on spacelike and timelike surface in the same space, their some new properties are presented by the aid of the focal surfaces obtained. Lastly, by generalizing the Backlund and integrability theorems done in the Minkowski 3-space, new interesting results are gotten.