Golden Riemannian Manifolds Having Constant Sectional Curvatures and Their Submanifolds

We study Golden Riemannian manifolds having constant sectional curvatures. First of all, we observed that if the Golden manifold has a constant (real) sectional curvature, then under certain conditions it is flat. Then, we examined holomorphic-like and holomorphic bisectional-like sectional curvatures. We have found that these both curvatures are zero on Golden Riemannian manifolds. Therefore, we have modified these notions by introducing the notion of Golden sectional curvature and we provide an example for this new notion. We then obtain the expression of curvature tensor field when the Golden sectional curvature is constant. Moreover, we applied this notion to submanifolds of Golden Riemannian manifolds and obtain existence theorems for semi-invariant submanifolds.