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Characterization of Parallel Isometric Immersions of Space Forms into Space Forms in the Class of Isotropic Immersions
Published online by Cambridge University Press: 20 November 2018
Abstract
For an isotropic submanifold ${{M}^{n}}(n\underline{\underline{>}}3)$ of a space form
${{\tilde{M}}^{n+p}}(c)$ of constant sectional curvature
$c$, we show that if the mean curvature vector of
${{M}^{n}}$ is parallel and the sectional curvature
$K$ of
${{M}^{n}}$ satisfies some inequality, then the second fundamental form of
${{M}^{n}}$ in
${{\tilde{M}}^{n+p}}$ is parallel and our manifold
${{M}^{n}}$ is a space form.
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- Copyright © Canadian Mathematical Society 2009