Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Characterizations of Focal Surfaces of A Tubular Surface in E^3   Here, we focus on focal surfaces of a tubular surface in Euclidean 3-space
E^3: Firstly, we give the tubular surfaces with respect to Frenet and Darboux
frames. Then, we define focal surfaces of these tubular surfaces. We get some
results for these types of surfaces to become flat and we show that there is no
minimal focal surface of a tubular surface in E^3. We give some examples for
these type surfaces. Further, we show that u-parameter curves cannot be
asymptotic curves and we obtain some results about v-parameter curves of the
focal surface M^*.

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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci