New sphere theorems under curvature operator of the second kind

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Investigation proves differentiable sphere theorems and curvature characterization in Riemannian manifolds, indicating new rigidity results.

Differentiable sphere theorems and curvature characterization achieved under specific curvature conditions.
Key findings include the relationship between curvature operator and eigenvalues in 3 and 4 dimensions.
Analysis conducted on Riemannian manifolds using optimal curvature criteria for rigidity results.
Highlights implications for generalization of prior works on curvature positivity and manifold characteristics.

Li et al. (2025) studied this question.

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Investigation proves differentiable sphere theorems and curvature characterization in Riemannian manifolds, indicating new rigidity results.