Biconservative surfaces in BCV-spaces

TL;DR

This paper characterizes biconservative surfaces within 3D BCV-spaces, focusing on cases with constant angle to the Hopf vector and SO(2)-invariance, expanding understanding of these geometrically significant hypersurfaces.

Contribution

It provides a detailed characterization of biconservative surfaces in BCV-spaces under specific symmetry and angle conditions, a novel contribution to differential geometry.

Findings

Characterization of biconservative surfaces with constant angle to Hopf vector field

Description of SO(2)-invariant biconservative surfaces in BCV-spaces

Extension of known results to new classes of hypersurfaces

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.