class_docstr: Class for (principal) fiber bundles.
  
  This class implements abstract methods for fiber bundles, or more
  generally manifolds, with a submersion map, or a right Lie group action.
  
  Parameters
  ----------
  group : LieGroup
      Group that acts on the total space by the right.
      Optional. Default : None.
      Either the group or the group action must be given.
  group_action : callable
      Right group action. It must take as input a point of the total space
      and an element of the group, and return a point of the total space.
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docstr: Compute the fundamental tensor A of the submersion.
  
  The fundamental integrability tensor A is defined for tangent vectors
  :math:`X = tangent\_vec\_a` and :math:`Y = tangent\_vec\_b` of the
  total space by [ONeill]_ as
  :math:`A_X Y = ver\nabla_{hor X} (hor Y) + hor \nabla_{hor X}( ver Y)`
  where :math:`hor, ver` are the horizontal and vertical projections
  and :math:`\nabla` is the connection of the total space.
  
  Parameters
  ----------
  tangent_vec_a : array-like, shape=[..., {total_space.dim, [n, m]}]
      Tangent vector at `base_point`.
  tangent_vec_b : array-like, shape=[..., {total_space.dim, [n, m]}]
      Tangent vector at `base_point`.
  base_point : array-like, shape=[..., {total_space.dim, [n, m]}]
      Point of the total space.
  
  Returns
  -------
  vector : array-like, shape=[..., {total_space.dim, [n, m]}]
      Tangent vector at `base_point`, result of the A tensor applied to
      `tangent_vec_a` and `tangent_vec_b`.
  
  References
  ----------
  .. [ONeill]  O’Neill, Barrett. The Fundamental Equations of a
      Submersion, Michigan Mathematical Journal 13, no. 4
      (December 1966): 459–69. https://doi.org/10.1307/mmj/1028999604.
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code: def integrability_tensor(
      self, tangent_vec_a, tangent_vec_b, base_point
  ):
      r"""Compute the fundamental tensor A of the submersion.
  
      The fundamental integrability tensor A is defined for tangent vectors
      :math:`X = tangent\_vec\_a` and :math:`Y = tangent\_vec\_b` of the
      total space by [ONeill]_ as
      :math:`A_X Y = ver\nabla_{hor X} (hor Y) + hor \nabla_{hor X}( ver Y)`
      where :math:`hor, ver` are the horizontal and vertical projections
      and :math:`\nabla` is the connection of the total space.
  
      Parameters
      ----------
      tangent_vec_a : array-like, shape=[..., {total_space.dim, [n, m]}]
          Tangent vector at `base_point`.
      tangent_vec_b : array-like, shape=[..., {total_space.dim, [n, m]}]
          Tangent vector at `base_point`.
      base_point : array-like, shape=[..., {total_space.dim, [n, m]}]
          Point of the total space.
  
      Returns
      -------
      vector : array-like, shape=[..., {total_space.dim, [n, m]}]
          Tangent vector at `base_point`, result of the A tensor applied to
          `tangent_vec_a` and `tangent_vec_b`.
  
      References
      ----------
      .. [ONeill]  O’Neill, Barrett. The Fundamental Equations of a
          Submersion, Michigan Mathematical Journal 13, no. 4
          (December 1966): 459–69. https://doi.org/10.1307/mmj/1028999604.
      """
      raise NotImplementedError
  
file_path: geomstats/geomstats/geometry/fiber_bundle.py
imports: import sys
  from abc import ABC
  from scipy.optimize import minimize
  import geomstats.backend
  from geomstats.vectorization import get_batch_shape
label_desc: Use image node_id 11 for calling the FiberBundle obj's underlying member method code with example usage: obj.integrability_tensor(tangent_vec_a, tangent_vec_b, base_point) without return types