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arXiv · 2408.07359

Intrinsic characterizations of biconservative surfaces in the 4-dimensional hyperbolic space

Simona Nistor·Mihaela Rusu
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Abstract

In this paper, we extend the investigation of biconservative surfaces with parallel normalized mean curvature vector fields (PNMC) in the 4-dimensional space forms, focusing on the hyperbolic space \mathbb{H}^4, the last remaining case to explore. We establish that an abstract surface admits a PNMC biconservative immersion in \mathbb{H}^4 if and only if it satisfies a certain intrinsic condition; if such an immersion exists, it is unique. We further analyze these abstract surfaces, showing that they form a two-parameter family. Additionally, we provide three characterizations of the intrinsic condition to explore the geometric properties of these surfaces.

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Simona Nistor, Mihaela Rusu. 2024-08-14. Intrinsic characterizations of biconservative surfaces in the 4-dimensional hyperbolic space. https://arxiv.org/abs/2408.07359

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