2019/11/05 by M. Dajczer, Dajczer, M., Miguel I. Jimenez +1
Mathematics · Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Myofascial pain diagnosis and treatment
paper · pdf · doi:10.48550/arxiv.1911.01863
This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of isometric immersions in Euclidean space, we prove that a system of three equations for a certain pair of tensors are the integrability conditions for the differential equation that determines the infinitesimal variations. In addition, we give some rigidity results when the submanifold is intrinsically a Riemannian product of manifolds.