Theorems · Theorem · global analysis

Bundle.ContMDiffRiemannianMetric.symm

∀ {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]
  (self : Bundle.ContMDiffRiemannianMetric IB n F E) (b : B) (v w : E b), ((self.inner b) v) w = ((self.inner b) w) v

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Riemannian

Cited by

0 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceAddCommGroupModuleFiberBundleVectorBundle