2007/06/21 by Labbi M. L, Labbi M. -L, -L, Labbi M. · 1 citation
Mathematics · Physics and Astronomy · #53C40 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C40 #msc:53C42
paper · pdf · doi:10.48550/arxiv.0706.3092
18 pages
arxiv created 2007/06/21 · openalex publication_date 2007/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recall that a submanifold of a Riemannian manifold is said to be minimal if its mean curvature is zero. It is classical that minimal submanifolds are the critical points of the volume function. In this paper, we examine the critical points of the total (2k)-th Gauss-Bonnet curvature function, called (2k)-minimal submanifolds. We prove that they are characterized by the vanishing of a higher mean curvature, namely the (2k+1)-Gauss-Bonnet curvature. Furthermore, we show that several properties of usual minimal submanifolds can be naturally generalized to (2k)-minimal submanifolds.