Semi riemann manifolds conjugate point and variation calculus

This thesis is prepared in four sections. In the first section, Rudiments about the thesis are given. In the second section neccessary essential notions are explained. In the third section, the variation of the curves which are taken on any fields and Jacobi fields are defined. At that time, the Jacobi equation which is known for the fields of speed vectors and the jacobi equation which is related to the length of the field of the speed vectors are used equivalent to each other in literature. This thesis has given that there is a possible transition between two equations. These two equations are called Jacobi equation without marking off. The conjugate points on a surface of along a geodesic are researched in this thesis. From there, focal points are defined on the semi-Riemann manifolds and second variation formullas, are given. In the fourth section is taken partly indepentable from other sections. In this section after giving a summary of parallel surfaces, some orginal results are gained related to the conjugate points. It can be acceptable as characterisations of the properties of being a geodesic, conjugate point, etc. On the corresponding parallel surfaces. These characterisations that are given in the fourth section, don't exist in literature, they are orginals. The references and the index of the words are added at the end of this thesis. This thesis contains ninetyone pages and twentytwo shapes