Nullity conditions in paracontact geometry


Thesis Type: Doctorate

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2016

Thesis Language: Turkish

Student: İREM KÜPELİ ERKEN

Supervisor: CENGİZHAN MURATHAN

Abstract:

In this thesis, there are 5 chapters. The first chapter is devoted to the introduction. Second chapter contains some well-known definitions and results which will be used in other chapters. In the third chapter, the features of almost paracontact manifolds and almost paracontact metric manifolds were examined. The torsion tensor field of almost paracontact manifold was defined and on manifold the normal structure was constructed. Also a K-paracontact manifold was defined and some properties were given to be a K-paracontact manifold. Also para-Sasakian manifold was introduced and properties were given. In this chapter paracontact manifolds curvature properties and Legendrian foliations were also studied. The fourth section contains paracontact (k,m)-manifolds and has three subsection. First section is devoted to basic definitions and theorems about paracontact (k,m)-manifolds, second subsection is devoted to paracontact (k,m)-manifolds with k>-1 and third subsection is related to paracontact (k,m)-manifolds with k<-1 . In the fifth section, we deal with 3-dimensional paracontact (k,m,v)-manifolds. In this section, there are three subsection. First subsection is devoted to preliminary results on (2n+1)-dimensional paracontact metric (k,m,v)-manifolds. Second subsection is related to classification of the 3-dimensional paracontact metric (k,m,v)-manifolds. Finally, we gave an application in the third subsection.