Some surfaces with respect to semi-symmetric metric and non-metric connections in 3-dimensional euclidean space

This thesis consists of four chapters. In the first chapter, the aim and scope of the study are presented, followed by fundamental concepts of differential geometry. The historical background, definitions, and applications of Monge surfaces and translation surfaces are also discussed. The second chapter provides the basic definitions and theorems related to surface theory and the notion of connection. In particular, various types of semi-symmetric connections are examined to establish the theoretical framework of the study. In the third chapter, Monge and translation surfaces are investigated under semi-symmetric metric connections. The unit normal vectors, coefficients of the first fundamental form, and mean curvatures of the surfaces are computed. Moreover, the conditions under which these surfaces are minimal are explored. The fourth chapter focuses on the analysis of the same surfaces under semi-symmetric non-metric connections. This study aims to reveal how different types of connections affect the mean curvature of surfaces, thereby demonstrating how surface geometry varies depending on the chosen connection. Keywords: Minimal surface, Monge surface, Translation surface, Semi-symmetric metric connection, Semi-symmetric non-metric connection.