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Characterization of Parallel Isometric Immersions of Space Forms into Space Forms in the Class of Isotropic Immersions
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- Journal:
- Canadian Journal of Mathematics / Volume 61 / Issue 3 / 01 June 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 641-655
- Print publication:
- 01 June 2009
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- Article
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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.
