Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Natural Metrics on the Tangent Bundle   Natural metrics provide a way to induce a metric on the tangent bundle from
the metric on its base manifold. The most studied type is the Sasaki metric,
which applies the base metric separately to the vertical and horizontal
components. We study a more general class of metrics which introduces
interactions between the vertical and horizontal components, with scalar
weights. Additionally, we explicitly clarify how to apply our and other induced
metrics on the tangent bundle to vector fields where the vertical component is
not constant along the fibers. We give application to the Special Orthogonal
Group SO(3) as an example.

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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
19
The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph