Isometric embeddings of finite-dimensional p ell _p -spaces over the quaternions Academic Article uri icon


  • The nonexistence of isometric embeddings (Formulas Presented) with p q is proved. The only exception is q = 2, p 2, in which case an isometric embedding exists if n is sufficiently large, n N(m, p). Some lower bounds for N(m, p) are obtained by using the equivalence between the isometric embeddings in question and the cubature formulas for polynomial functions on projective spaces. Even though only the quaternion case is new, the exposition treats the real, complex, and quaternion cases simultaneously. 2004 American Mathematical Society.

published proceedings

  • St Petersburg Mathematical Journal

author list (cited authors)

  • Lyubich, Y. I., & Shatalova, O. A.

citation count

  • 8

complete list of authors

  • Lyubich, Yu I||Shatalova, OA

publication date

  • January 2004