Index one minimal surfaces in positively curved 3-manifolds

2020/02/17 by Antonio R�os, Ros, Antonio
Mathematics · #53A10 #57M50 #58E12 #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.2002.07276

openalex publication_date 2020/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We construct a Riemannian metric of positive sectional curvature on the 3-dimensional projective space with a two-sided closed embedded minimal surface of genus 3, index 1 and nullity 0.

Citations

• The unknottedness of minimal embeddings
• On the existence of minimal Heegaard surfaces

Related

• Singular limit laminations, Morse index, and positive scalar curvature
• Closed minimal surfaces of high Morse index in manifolds of negative curvature
• Second variation of one-sided complete minimal surfaces
• Minimal spheres of arbitrarily high Morse index
• Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature