Theorems · Definition · global analysis

Bundle.ContMDiffRiemannianMetric.inner

{EB : Type u_1} →
  [inst : NormedAddCommGroup EB] →
    [inst_1 : NormedSpace ℝ EB] →
      {HB : Type u_2} →
        [inst_2 : TopologicalSpace HB] →
          {IB : ModelWithCorners ℝ EB HB} →
            {n : WithTop ℕ∞} →
              {B : Type u_3} →
                [inst_3 : TopologicalSpace B] →
                  [inst_4 : ChartedSpace HB B] →
                    {F : Type u_4} →
                      [inst_5 : NormedAddCommGroup F] →
                        [inst_6 : NormedSpace ℝ F] →
                          {E : B → Type u_5} →
                            [inst_7 : TopologicalSpace (Bundle.TotalSpace F E)] →
                              [inst_8 : (b : B) → TopologicalSpace (E b)] →
                                [inst_9 : (b : B) → AddCommGroup (E b)] →
                                  [inst_10 : (b : B) → Module ℝ (E b)] →
                                    [inst_11 : FiberBundle F E] →
                                      [inst_12 : VectorBundle ℝ F E] →
                                        Bundle.ContMDiffRiemannianMetric IB n F E → (b : B) → E b →L[ℝ] E b →L[ℝ] ℝ

The scalar product along the fibers of the bundle.

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Riemannian

Cited by

4 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceAddCommGroupModuleFiberBundleVectorBundle