Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On extrinsic geometry of unit normal vector fields of Riemannian
  hyperfoliations   We consider a unit normal vector field of (local) hyperfoliation on a given
Riemannian manifold as a submanifold in the unit tangent bundle with Sasaki
metric. We give an explicit expression of the second fundamental form for this
submanifold and a rather simple condition its totally geodesic property in the
case of a totally umbilic hyperfoliation. A corresponding example shows the
non-triviality of this condition. In the 2-dimensional case, we give a complete
description of Riemannian manifolds admitting a geodesic unit vector field with
totally geodesic property.

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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas