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arxiv: 1103.1615 · v1 · pith:ZFNAPW2Wnew · submitted 2011-03-08 · 🧮 math.DG

A splitting theorem for higher order parallel immersions

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keywords immersionsparallelflatorderclassconsiderconsistsdefined
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We consider isometric immersions into space forms having the second fundamental form parallel at order k. We show that this class of immersions consists of local products, in a suitably defined sense, of parallel immersions and normally flat immersions of flat spaces.

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