Theorems · Theorem · algebraic topology

Bundle.ContinuousRiemannianMetric.pos

∀ {B : Type u_4} [inst : TopologicalSpace B] {F : Type u_5} [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace ℝ F]
  {E : B → Type u_6} [inst_3 : TopologicalSpace (Bundle.TotalSpace F E)] [inst_4 : (b : B) → TopologicalSpace (E b)]
  [inst_5 : (b : B) → AddCommGroup (E b)] [inst_6 : (b : B) → Module ℝ (E b)] [inst_7 : FiberBundle F E]
  [inst_8 : VectorBundle ℝ F E] (self : Bundle.ContinuousRiemannianMetric F E) (b : B) (v : E b),
  v ≠ 0 → 0 < ((self.inner b) v) v

Defined in

Mathlib.Topology.VectorBundle.Riemannian

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceAddCommGroupModuleFiberBundleVectorBundle