5 citations · 18 across the 13 of their papers we have counts for
13 papers
Normal curvature bounds for immersions into Riemannian domains
Matteo Raffaelli
We study Gromov's problem on the minimal normal curvature of immersions. Our main result is a lower bound for the average normal curvature of a closed submanifold immersed in a Rie…
Total absolute curvature and rigidity of surfaces in Cartan-Hadamard manifolds
Mohammad Ghomi, Joseph Ansel Hoisington, Matteo Raffaelli +1
We show that closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies. This generalizes Chern-Lashof's theorem for surfaces in…
Total torsion of three-dimensional lines of curvature
Matteo Raffaelli
A curve in a Riemannian manifold is three-dimensional if its torsion (signed second curvature function) is well-defined and all higher-order curvatures vanish identically.…
Existence of optimal flat ribbons
Simon Blatt, Matteo Raffaelli
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in can be extended to an infinitely narrow flat ribbon having mini…
Differential geometry of space curves: Forgotten chapters
Dmitry Fuchs, Ivan Izmestiev, Matteo Raffaelli +2
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified trea…
Classification of rank-one submanifolds
Matteo Raffaelli
We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold , we associate an integer-valued function, called degree, measuring the extent to…
Planar pseudo-geodesics and totally umbilic submanifolds
Steen Markvorsen, Matteo Raffaelli
We study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel nor…
Nonrigidity of flat ribbons
Matteo Raffaelli
We study ribbons of vanishing Gaussian curvature, i.e., flat ribbons, constructed along a curve in . In particular, we first investigate to which extent the ruled s…
Curvature-adapted submanifolds of semi-Riemannian groups
Margarida Camarinha, Matteo Raffaelli
We study semi-Riemannian submanifolds of arbitrary codimension in a Lie group equipped with a bi-invariant metric. In particular, we show that, if the normal bundle of $M \subs…
Flat approximations of hypersurfaces along curves
Irina Markina, Matteo Raffaelli
Given a smooth curve in some -dimensional surface in , we study existence and uniqueness of a flat surface having the same field of normal vectors…
The geometric Cauchy problem for rank-one submanifolds
Matteo Raffaelli
Given a smooth distribution of -dimensional planes along a smooth regular curve in , we consider the following problem: to find an -dimens…
The convex hull of a convex space curve with four vertices
Jakob Bohr, Steen Markvorsen, Matteo Raffaelli
We obtain an upper bound for the volume of the convex hull of a simple closed Frenet curve with exactly four vertices, i.e., four points of vanishing torsion, and lying on the boun…
Cartan ribbonization and a topological inspection
Matteo Raffaelli, Jakob Bohr, Steen Markvorsen
We develop the concept of Cartan ribbons together with a rolling-based method to ribbonize and approximate any given surface in space by intrinsically flat ribbons. The rolling req…