Work

PMC Biconservative Surfaces in Complex Space Forms

Year: 2021

Type: preprint

Abstract: In this article we consider PMC surfaces in complex space forms, and we study the interaction between the notions of PMC, totally real and biconservative. We first consider PMC surfaces in non-flat complex space forms and we prove that they are biconservative if and only if totally real. Then, we find a Simons type formula for a well-chosen vector field constructed from the mean curvature vector field. Next, we prove a rigidity result for CMC biconservative surfaces in 2-dimensional complex space forms. We prove then a reduction codimension result for PMC biconservative surfaces in non-flat complex space forms. We conclude by constructing from the Segre embedding examples of CMC non-PMC biconservative submanifolds, and we also discuss when they are proper-biharmonic.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2107.11558

Authors: Bibi, Hiba, Chen, Bang-Yen, Fetcu, Dorel, Oniciuc, Cezar

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii, Colegiul Consultativ pentru Cercetare-Dezvoltare şi Inovare

OpenAlex ID: W3185074271

Cites: 37

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Related to: 20