class_docstr: Open hemisphere.
  
  An open set of the hypersphere where the first coordinate is always
  positive.
  
  .. math::
  
      \mathrm{HS}^{k-1}=\left\{x \in \mathbb{R}^k: \|x\|=1
      \text { and } x_0>0\right\}
class_docstr_tok: ["Open","hemisphere",".","An","open","set","of","the","hypersphere","where","the","first","coordinate","is","always","positive",".","..","math",":",":","\\mathrm","{","HS","}","^","{","k-1","}","=\\left\\","{","x","\\in","\\mathbb","{","R","}","^k",":","\\|x\\|=1","\\text","{","and","}","x_0",">","0\\right\\","}"]
docstr: Metric to equip the space with if equip is True.
docstr_tok: ["Metric","to","equip","the","space","with","if","equip","is","True","."]
code: def default_metric():
      """Metric to equip the space with if equip is True."""
      return OpenHemispherePullbackMetric
  
imports: import geomstats.backend
  from geomstats.geometry.base import OpenSet
  from geomstats.geometry.diffeo import Diffeo
  from geomstats.geometry.hyperboloid import Hyperboloid
  from geomstats.geometry.hypersphere import Hypersphere
  from geomstats.geometry.product_manifold import ProductManifold, ProductRiemannianMetric
  from geomstats.geometry.pullback_metric import PullbackDiffeoMetric
label_desc: Use image node_id 2 for calling the OpenHemisphere obj's underlying member method code with example usage: obj.default_metric() and returns: OpenHemispherePullbackMetric