Spherical submanifolds in a Euclidean space

  title={Spherical submanifolds in a Euclidean space},
  author={Haila Alodan and Sharief Deshmukh},
  journal={Monatshefte f{\"u}r Mathematik},
Abstract.In this paper, we are interested in extending the study of spherical curves in R3 to the submanifolds in the Euclidean space Rn+p. More precisely, we are interested in obtaining conditions under which an n-dimensional compact submanifold M of a Euclidean space Rn+p lies on the hypersphere Sn+p−1(c) (standardly imbedded sphere in Rn+p of constant curvature c). As a by-product we also get an estimate on the first nonzero eigenvalue of the Laplacian operator Δ of the submanifold (cf… CONTINUE READING