Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to
  Mannheim Offsets of Timelike Ruled Surfaces   In this paper, we introduce the dual geodesic trihedron (dual Darboux frame)
of a timelike ruled surface. By the aid of the E. Study Mapping, we consider
timelike ruled surfaces as dual hyperbolic spherical curves and define the
Mannheim offsets of timelike ruled surfaces by means of dual Darboux frame. We
obtain the relationships between invariants of Mannheim timelike surface
offsets. Furthermore, we give the conditions for these surface offsets to be
developable.

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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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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: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: nlin