The scalar curvature of CR submanifold of maximal CR dimension with a conformal change

Abstract

In this paper, we investigate the codimension reduction theorem for an n-dimensional submanifold of an (n + p)-dimensional manifold (M, ~g) with a conformal change g = exp(–f)g where g denotes the Fubini-study metric on (n + p)-dimensional complex projective space P n+p/2 (C). Moreover, we tend to calculate the scalar curvature of an n-dimensional CR submanifold of maximal CR dimension of (M; g) and achieve the sufficient conditions for the existence of a totally geodesic submanifold M0 that includes M.