On statistical manifolds

The first chapter of this master's thesis, which consists of four chapters, has reserved for an introduction to literature review. The second chapter has some basic definitions and theorems for a better understanding of the other chapter, which consists of two subsections called Riemann manifolds and Riemann submersions.Tensors defined by O'Neill in Riemann submersions has been introduced. The properties, geometric meanings and covariant derivatives of these tensors have been studied. The third and fourth chapters have constituted the main part of the thesis: In the third chapter, statistical manifolds have introduced, their curvatures and properties have mentioned. In the fourth chapter, after statistical submersions and cosimplectic-like statistical submersions have given, the anti-invariance of cosymplectic-like statistical submersions has examined, supported by an example, and integrability and totally geodesicness of the distributions on the total space have obtained. Keywords: Statistical Structure, Affine Connection, Conjugate Connection.