2022/04/24 by Sergio Chion, Chion, S., M. Dajczer +1
Mathematics · #53B25 #53B35 #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.2204.11287
openalex publication_date 2022/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f\colon M2n→ℝ2n+4 be an isometric immersion of a Kaehler manifold of complex dimension n≥ 5 into Euclidean space with complex rank at least 5 everywhere. Our main result is that, along each connected component of an open dense subset of M2n, either f is holomorphic in ℝ2n+4≅ℂn+2 or it is in a unique way a composition f=F∘ h of isometric immersions. In the latter case, we have that h\colon M2n→ N2n+2 is holomorphic and F\colon N2n+2→ℝ2n+4 belongs to the class, by now quite well understood, of non-holomorphic Kaehler submanifold in codimension two. Moreover, the submanifold F is minimal if and only if f is minimal.