2016/01/10 by Kamil Niedzialomski, Niedzialomski, Kamil
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.1601.02248
20 pages; major revision; all mistakes corrected
arxiv created 2017/03/11 · arxiv updated 2017/03/14
We extend the notion of r-minimality of a submanifold in arbitrary codimension to u-minimality for a multi-index u∈ℕq, where q is the codimension. This approach is based on the analysis on the frame bundle of orthonormal frames of the normal bundle to a submanifold and vector bundles associated with this bundle. The notion of u-minimality comes from the variation of σu-symmetric function obtained from the family of shape operators corresponding to all possible bases of the normal bundle. We obtain the variation field, which gives alternative definition of u--minimality. Finally, we give some examples of u-minimal submanifolds for some choices of u.