Austere Submanifolds in Complex Projective Space

2014/02/21 by Marianty Ionel, Thomas A. Ivey, Ionel, Marianty +2
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1402.5334

13 pages; final version, to appear in Communications in Analysis and Geometry

openalex publication_date 2014/02/21 · arxiv created 2015/08/14 · arxiv updated 2015/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an arbitrary submanifold M ⊂ ℂPⁿ we determine conditions under which it is austere, i.e., the normal bundle of M is special Lagrangian with respect to Stenzel's Ricci-flat Kähler metric on TℂPⁿ. We also classify austere surfaces in ℂPⁿ.

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