2023/12/05 by Theodoros Vlachos, Vlachos, Theodoros
Mathematics · #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2312.02876
openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the geometry and topology of compact submanifolds of arbitrary codimension in space forms satisfying a certain pinching condition involving the length of the second fundamental form and the mean curvature. We prove that this pinching condition either forces homology to vanish in a range of intermediate dimensions, or completely determines the submanifold up to congruence. The results are sharp and extend previous results due to several authors without imposing any further assumption on the mean curvature.