# On biconservative hypersurfaces in 4-dimensional Riemannian space forms

## TL;DR

This paper classifies biconservative hypersurfaces with three distinct principal curvatures in 4-dimensional Riemannian space forms, specifically in spheres and hyperbolic spaces, providing explicit descriptions.

## Contribution

It offers the first complete explicit classification of such hypersurfaces in 4-dimensional space forms with exactly three principal curvatures.

## Key findings

- Classification of biconservative hypersurfaces in S^n and H^n
- Explicit descriptions of hypersurfaces with three principal curvatures
- New insights into geometric properties of these hypersurfaces

## Abstract

In this paper, we study biconservative hypersurfaces in $\mathbb S^{n}$ and $\mathbb H^{n}$. Further, we obtain complete explicit classification of biconservative hypersurfaces in $4$-dimensional Riemannian space form with exactly three distinct principal curvatures.