Biconservative surfaces

TL;DR

This paper explores the geometric properties of biconservative surfaces in Riemannian manifolds, focusing on their relationship with holomorphicity and providing a full classification of constant mean curvature biconservative surfaces in four-dimensional space forms.

Contribution

It offers new insights into the geometry of biconservative surfaces and classifies CMC biconservative surfaces in 4D space forms, linking them to holomorphic functions.

Findings

Relationship between biconservative surfaces and holomorphicity of a generalized Hopf function

Complete classification of CMC biconservative surfaces in 4D space forms

Geometric properties of biconservative surfaces in Riemannian manifolds

Abstract

In this work we obtain some geometric properties of biconservative surfaces into a Riemannian manifold. In particular, we shall study the relationship between biconservative surfaces and the holomorphicity of a generalized Hopf function. Also, we give a complete classification of CMC biconservative surfaces in a $4$-dimensional space form.