Statistical and warped product manifolds


Thesis Type: Postgraduate

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2011

Thesis Language: Turkish

Student: ERKAN KORKMAZ

Supervisor: CENGİZHAN MURATHAN

Abstract:

This thesis fundamentally consists of five chapters. The first chapter has been devoted to the introduction. In the second chapter, for using in the other chapters, some main definitions, examples and theorems have been given. In the third chapter, the Fisher Information metric was defined for constructing a geometry in statistica models. Some results were obtained with helping expected value and potential function for Gamma 2- manifold and Gaussian 2-manifold. In the fourth chapter, some concepts have been given for manifolds and connections. And with the help of these concepts, statistical manifold were defined. The values of components of connection were calculated in Gamma and Gaussian manifolds. We defined conjugate connections and some properties were given about Riemannian curvature. In the fifth chapter, some main concepts about warped products have been given. Original results were found about conjugate connections in double warped product manifold. The equations about Riemannian curvature were calculated in double warped product manifold. With the help of these equations some results were found about the concept of dually flat.