On the geometry of almost α-cosymplectic f-manifolds

This thesis consists of six chapters. In the first chapter, the motivation of the problems and their background are presented. In the second chapter, we give some notions and definitions which will be used in the others chapters. In the third chapter, we define the invariant submanifold of almost α-cosymplectic f-manifolds. We have investigate the curvature properties and have given some results for invariant submanifolds of almost α-cosymplectic f-manifolds. We also present some theorems for semi-invariant submanifolds of almost α-cosymplectic f-manifolds and investigate the integrability of the distributions. In the fourth chapter, we define almost α-cosymplectic f-manifolds endowed with a quarter-symmetric metric connection. We have calculated the curvature, the Ricci tensor and the scaler curvature with respect to a quarter-symmetric metric connection. Moreover, we show that there is not generalized recurrent, ϕ-recurrent α-cosymplectic f-manifolds. In the fifth chapter, we introduce almost α-cosymplectic f-manifolds endowed with a semi-symmetric non-metric connection. We also investigate the Riemann curvature tensor field, the ricci tensor field and give some theorems for almost α-cosymplectic f-manifolds. In the sixth chapter, we define semi-invariant submanifold of almost α-cosymplectic f-manifolds endowed with a semi-symmetric non-metric connection and obtain some results. Moreover, we obtain the integrability of distributions and their results. KEYWORDS: Almost α- cosymplectic f-manifolds, quarter symmetric metric connection, invariant submanifold, semi-invariant submanifold, semi-symmetric nonmetric connection.