Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On focal submanifolds of isoparametric hypersurfaces and Simons formula   The focal submanifolds of isoparametric hypersurfaces in spheres are all
minimal Willmore submanifolds, mostly being $\mathcal{A}$-manifolds in the
sense of A.Gray but rarely Ricci-parallel (\cite{QTY},\cite{LY},\cite{TY3}). In
this paper we study the geometry of the focal submanifolds via Simons formula.
We show that all the focal submanifolds with $g\geq3$ are not normally flat by
estimating the normal scalar curvatures. Moreover, we give a complete
classification of the semiparallel submanifolds among the focal submanifolds.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex