2000/04/14 by Isabel M. C. Salavessa, Salavessa, Isabel M. C., Giorgio Valli +1 · 1 citation
Mathematics · Physics and Astronomy · #32C17 #53A10 #53C15 #53C42 #53C55 #58E20 #58F05 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:32C17 #msc:53A10 #msc:53C15 #msc:53C42 #msc:53C55 #msc:58E20 #msc:58F05
paper · pdf · doi:10.48550/arxiv.math/0004093
17 pages, plain LaTeX
arxiv created 2000/04/14 · openalex publication_date 2000/04/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define broadly-pluriminimal immersed 2n-submanifold F: M --> N into a Kaehler-Einstein manifold of complex dimension 2n and scalar curvature R. We prove that, if M is compact, n ≥ 2, and R < 0, then: (i) Either F has complex or Lagrangian directions; (ii) If n = 2, M is oriented, and F has no complex directions, then it is a Lagrangian submanifold, generalising the well-known case n = 1 for minimal surfaces due to Wolfson. We also prove that, if F has constant Kaehler angles with no complex directions, and is not Lagrangian, then R = 0 must hold. Our main tool is a formula on the Laplacian of a symmetric function on the Kaehler angles.