In this study, the serum vitamin E (total tocopherol) levels in patients with breast cancer (n = 100) and healthy controls (n = 70) were measured. The mean values for vitamin E were found to be 0.44 mg/100 ml in breast cancer patients and 1.108 mg/100 ml in controls. In the statistical evaluation, the vitamin E levels in breast cancer patients are significantly lower than in the controls (P < 0.05). The influence of factors such as suckling period, age of first gestation, smoking status and dietary habits were also studied.

Our paper aims to study the geometry of submanifolds of an almost-complex metallic manifold. We give an example of this type of manifold, and reveal the fundamental properties of structure induced on submanifolds. We establish subsets of submanifolds in almost-complex metallic manifolds, such as invariant, anti-invariant, and slant submanifolds.