Rotational submanifolds in Euclidean spaces

Abstract

The rotational embedded submanifold was first studied by Kuiper as a submanifold in [Formula: see text]. The generalized Beltrami submanifolds and toroidal submanifold are the special examples of these kind of submanifolds. In this paper, we consider [Formula: see text]-dimensional rotational embedded submanifolds in Euclidean [Formula: see text]-space [Formula: see text]. We give some basic curvature properties of this type of submanifolds. Further, we obtain some results related with the scalar curvature and mean curvature of these submanifolds. As an application, we give an example of rotational submanifold in [Formula: see text].