Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypersurfaces of Product Spaces with a Canonical Direction   Consider a complete Riemannian manifold $M^n$ and let $\Sigma^n$ be an
orientable hypersurface of the product manifold $M\times\mathbb{R}$ endowed
with its standard product metric $\langle \,,\, \rangle.$ Let $\nabla\xi$
denote the gradient of the height function $\xi$ of $\Sigma.$ In this note, we
characterize the hypersurfaces $\Sigma$ which have $\nabla\xi$ as a principal
direction. Our approach is based on the work of R. Tojeiro, who considered the
case where $M$ is a constant sectional curvature space form.

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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga