Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourth Fundamental Form and $i$-th Curvature Formulas in
  ${\mathbb{E}}^{4}$   We introduce fourth fundamental form $IV,$ and $i$-th curvature formulas of
hypersurfaces in the four dimensional Euclidean geometry ${\mathbb{E}}^{4}$.
Defining fourth fundamental form and $i$-th curvatures for hypersurfaces, we
calculate them on rotational hypersurface. In addition we study rotational
hypersurface satisfying $\Delta ^{IV}\mathbf{x=Ax}$ for some $4\times 4$ matrix
$\mathbf{A.}$

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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th