On Jacobi Field Splitting Theorems
Dennis Gumaer, Frederick Wilhelm
TL;DR
This paper extends Jacobi field splitting theorems to manifolds with positive sectional and intermediate Ricci curvatures, broadening their applicability in Riemannian geometry.
Contribution
It introduces new splitting theorems for Jacobi fields under positive curvature conditions, generalizing Wilking's original results.
Findings
Extended splitting theorems to positive sectional curvature
Generalized to positive and nonnegative intermediate Ricci curvatures
Broadened understanding of geometric structures under curvature constraints
Abstract
We formulate extensions of Wilking's Jacobi field splitting theorem to uniformly positive sectional curvature and also to positive and nonnegative intermediate Ricci curvatures.
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