Showing papers by "Stefano Montaldo published in 2018"
TL;DR: In this article, the main aim of this work is to construct several new families of proper biharmonic functions defined on open subsets of the classical compact simple Lie groups, which connect our work with the theory of submersive harmonic morphisms, and use this to interpret our new examples on the Euclidean sphere and on the hyperbolic space.
Abstract: The main aim of this work is to construct several new families of proper biharmonic functions defined on open subsets of the classical compact simple Lie groups $$\mathbf{SU}(n)$$
, $$\mathbf{SO}(n)$$
and $$\mathbf{Sp}(n)$$
. We work in a geometric setting which connects our study with the theory of submersive harmonic morphisms. We develop a general duality principle and use this to interpret our new examples on the Euclidean sphere $${\mathbb S}^3$$
and on the hyperbolic space $${\mathbb H}^3$$
.
22 citations
TL;DR: In this article, it was shown that the canonical inclusion i : S n − 1 (R ) ↪ S n is a proper r -harmonic submanifold of S n if and only if the radius R is equal to 1 / r.
22 citations
TL;DR: In this article, the existence of proper r-harmonic submanifolds into ellipsoids and rotation hypersurfaces was proved and several new, proper r -harmonic subsets of Riemannian manifolds were constructed.
Abstract: The study of r -harmonic maps was proposed by Eells–Sampson in 1965 and by Eells–Lemaire in 1983. These maps are a natural generalization of harmonic maps and are defined as the critical points of the r -energy functional E r ( φ ) = ( 1 ∕ 2 ) ∫ M | ( d ∗ + d ) r ( φ ) | 2 d v M , where φ : M → N denotes a smooth map between two Riemannian manifolds. If an r -harmonic map φ : M → N is an isometric immersion and it is not minimal, then we say that φ ( M ) is a proper r -harmonic submanifold of N . In this paper we prove the existence of several new, proper r -harmonic submanifolds into ellipsoids and rotation hypersurfaces.
17 citations
TL;DR: In this erratum first we amend the stability study of some proper biharmonic maps as discussed by the authors, which we consider in this paper. But we do not discuss the stability of these maps.
Abstract: In this erratum first we amend the stability study of some proper biharmonic maps
2 citations
TL;DR: In this paper, a characterization of proper biharmonic CMC surfaces in a 3D Riemannian manifold is given, where the fibers are the trajectories of a complete unit Killing vector field.
1 citations