Classification of codimension two deformations of rank two Riemannian\n manifolds

2015/03/09 by Luis A. Florit, Florit, Luis A., Guilherme Machado de Freitas +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #53B25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Myofascial pain diagnosis and treatment

paper · pdf · doi:10.48550/arxiv.1503.02624

openalex publication_date 2015/03/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The purpose of this work is to close the local deformation problem of rank\ntwo Euclidean submanifolds in codimension two by describing their moduli space\nof deformations. In the process, we provide an explicit simple representation\nof these submanifolds, a result of independent interest by its applications. We\nalso determine which deformations are genuine and honest, allowing us to find\nthe first known examples of honestly locally deformable rank two submanifolds\nin codimension two. In addition, we study which of these submanifolds admit\nisometric immersions as Euclidean hypersurfaces, a property that gives rise to\nseveral applications to the Sbrana-Cartan theory of deformable Euclidean\nhypersurfaces.\n

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