Quaternion Kaehlerian manifolds isometrically immersed in Euclidean space

Abstract

Let M M be a complete 4 n 4n -dimensional quaternion Kaehlerian manifold isometrically immersed in the ( 4 n + d ) (4n + d) -dimensional Euclidean space. In this note we prove that if d > n d > n , then M M is a Riemannian product Q m × P {Q^m} \times P , where Q m {Q^m} is the m m -dimensional quaternion Euclidean space ( m ⩾ n − d ) (m \geqslant n - d) and P P is a Ricci flat quaternion Kaehlerian manifold.