Quaternion Kaehlerian Manifolds Isometrically Immersed in Euclidean Space
Copyright policy )Quaternion Kaehlerian Manifolds Isometrically Immersed in Euclidean Space
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.
Ricci flat, Local submanifolds, Global submanifolds, isometric immersion, quaternion Kaehler manifold, Riemannian product
Ricci flat, Local submanifolds, Global submanifolds, isometric immersion, quaternion Kaehler manifold, Riemannian product
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