A splitting theorem for higher order parallel immersions

Details A splitting theorem for higher order parallel immersions A splitting theorem for higher order parallel immersions

2011-03-08

arxiv.org/abs/1103.1615v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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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