Showing papers by "Stefano Montaldo published in 2017"

Biconservative surfaces in BCV‐spaces

Abstract: Biconservative hypersurfaces are hypersurfaces with conservative stress-energy tensor with respect to the bienergy functional, and form a geometrically interesting family which includes that of biharmonic hypersurfaces. In this paper we study biconservative surfaces in the 3-dimensional Bianchi–Cartan–Vranceanu spaces, obtaining their characterization in the following cases: when they form a constant angle with the Hopf vector field; when they are SO(2)-invariant.

A Note on the Almansi Property

Abstract: The first goal of this note is to study the Almansi property on an m-dimensional model in the sense of Greene and Wu and, more generally, in a Riemannian geometric setting. In particular, we shall prove that the only model on which the Almansi property is verified is the Euclidean space $${\mathbb R}^m$$ . In the second part of the paper we shall study Almansi’s property and biharmonicity for functions which depend on the distance from a given submanifold. Finally, in the last section we provide an extension to the semi-Euclidean case $${\mathbb R}^{p,q}$$ which includes the proof of the classical Almansi property in $${\mathbb R}^m$$ as a special instance.

A note on the Almansi property

Abstract: The first goal of this note is to study the Almansi property on an m-dimensional model in the sense of Greene and Wu and, more generally, in a Riemannian geometric setting. In particular, we shall prove that the only model on which the Almansi property is verified is the Euclidean space R^m. In the second part of the paper we shall study Almansi's property and biharmonicity for functions which depend on the distance from a given submanifold. Finally, in the last section we provide an extension to the semi-Euclidean case R^{p,q} which includes the proof of the classical Almansi property in R^m as a special instance.