We consider Riemannian n-manifolds M with nontrivial κ-nullity “distribution” of the curvature
tensor R, namely, the variable rank distribution of tangent subspaces to M where R …

Let M be a complete Riemannian manifold and suppose p∈ M. For each unit vector v∈ T
p⁢ M, the Jacobi operator, 𝒥 v: v⊥→ v⊥ is the symmetric endomorphism, 𝒥 v⁢(w)= R⁢(w …

The curvature tensor is the most important isometry invariant of a Riemannian metric. We
study several related conditions on the curvature tensor to obtain topological and geo …