Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intrinsic Geometry and Director Reconstruction for Three-Dimensional
  Liquid Crystals   We give a description of the intrinsic geometry of elastic distortions in
three-dimensional nematic liquid crystals and establish necessary and
sufficient conditions for a set of functions to represent these distortions by
describing how they couple to the curvature tensor. We demonstrate that, in
contrast to the situation in two dimensions, the first-order gradients of the
director alone are not sufficient for full reconstruction of the director field
from its intrinsic geometry: it is necessary to provide additional information
about the second-order director gradients. We describe several different
methods by which the director field may be reconstructed from its intrinsic
geometry. Finally, we discuss the coupling between individual distortions and
curvature from the perspective of Lie algebras and groups and describe
homogeneous spaces on which pure modes of distortion can be realised.

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph