Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Teichm\"uller Space Is Totally Geodesic In Goldman Space   We construct a new Riemannian metric on Goldman space $\mathcal{B}(S)$, the
space of the equivalence classes of convex projective structures on the surface
$S$, and then prove the new metric, as well as the metric of Darvishzadeh and
Goldman, restricts to be the Weil-Petersson metric on Teichm$\ddot{u}$ller
space, embedded as a submanifold of Goldman space $\mathcal{B}(S)$. Moreover,
Teichm$\ddot{u}$ller space endowed with the Weil-Petersson metric then is
totally geodesic in the Riemannian manifold $\mathcal{B}(S)$.

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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat