On biconservative hypersurfaces in 4-dimensional Riemannian space forms. (English) Zbl 1422.53045
The present paper investigates in detail an interesting problem having an old source [D. Hilbert, “Die Grundlagen der Physik”, Math. Ann. 92, No. 1–2, 1–32 (1924; doi:10.1007/BF01448427)]. Recent results in the field of biconservative submanifolds are a justification for this study. The authors obtain some results on biconservative hypersurfaces in Riemannian space forms (complete explicit classification) and they try to clarify all biconservative hypersurfaces in \(S^4\) and \(H^4\). The exposition is clear and accurate.
Reviewer: Costache Apreutesei (Iaşi)
MSC:
| 53C40 | Global submanifolds |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
Keywords:
biconservative hypersurfaces; biharmonic submanifolds; null 2-type submanifolds; Riemannian space formsReferences:
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