r-Almost Newton-Ricci solitons immersed into a Riemannian manifold

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Cunha, Antonio W.¹  de Lima, Eudes L.²  de Lima, Henrique F.³ 

[1] Univ Fed Piaui, Dept Matemat, BR-64049550 Teresina, Piaui, Brazil

[2] Univ Fed Campina Grande, Unidade Acad Ciencias Exatas & Nat, BR-58900000 Cajazeiras, Paraiba, Brazil

[3] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil

关键词: Space forms;    r-Almost Newton-Ricci solitons;    Totally geodesic hypersurfaces;    Locally symmetric spaces;    Einstein manifolds;   

DOI  :  10.1016/j.jmaa.2018.04.026

来源: Elsevier

【 摘 要 】

We establish the new concept of r-almost Newton-Ricci soliton for hypersurfaces immersed in a Riemannian manifold, which involves the r-th Newton and the Ricci tensors and extends in a natural way the notion of immersed almost Ricci solitons introduced by Barros et al. [3]. In this setting, our purpose is to investigate the existence of these geometric objects. After exhibit some examples of r-almost Newton-Ricci solitons, we obtain sufficient conditions to guarantee that they must be totally geodesic under suitable constraints on the potential function and using appropriate maximum principles. Furthermore, a particular study of r-almost Newton-Ricci solitons immersed in a locally symmetric Einstein manifold is also made. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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