Contact -Submanifolds of an Odd-Dimensional Unit SphereReduction of the codimension of an isometric immersionOn hypersurfaces immersed in On some contact -submanifolds of an odd-dimensional unit sphereHomogeneity and some curvature condition for hypersurfacesOn harmonic and Killing vector fields

We study an (+1)(≥ 3)-dimensional contact -submanifold of (−1) contact -dimension in a (2+1)-unit sphere , and especially determine such submanifolds under the equality conditions appearing in (3.12). We also provide a sufficient condition in order for such a compact submanifold to be the model space given in the last Section 4.