PreprintCC BY 4.0arXiv
Biconservative hypersurfaces in space forms with harmonic curvature
Abstract
A biconservative hypersurface M in a space form M̅n+1(c) is a hypersurface whose normal part of the vector ΔH⃗ vanishes. We study such hypersurfaces with harmonic curvature or parallel Ricci curvature, and prove that have constant mean curvature. Also, by combining our results with previous results of H.B. Lawson Jr. and M. Umehara we obtain that if M is a biconservative hypersurface in a space form M̅n+1(c) with parallel Ricci tensor or harmonic curvature, then the shape operator boldA of M is covariant constant, i.e. ∇boldA=0.
Versions
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BibTeX
@misc{gupta2026biconservative,
title = {{Biconservative hypersurfaces in space forms with harmonic curvature}},
author = {Ram Shankar Gupta and Andreas Arvanitoyeorgos and Marina Statha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26376},
eprint = {2610.26376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26376},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Biconservative hypersurfaces in space forms with harmonic curvature
AU - Ram Shankar Gupta
AU - Andreas Arvanitoyeorgos
AU - Marina Statha
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26376
UR - https://arxiv.org/abs/2610.26376
AB - A biconservative hypersurface M in a space form M̅^n+1(c) is a hypersurface whose normal part of the vector ΔH⃗ vanishes. We study such hypersurfaces with harmonic curvature or parallel Ricci curvature, and prove that have constant mean curvature. Also, by combining our results with previous results of H.B. Lawson Jr. and M. Umehara we obtain that if M is a biconservative hypersurface in a space form M̅^n+1(c) with parallel Ricci tensor or harmonic curvature, then the shape operator boldA of M is covariant constant, i.e. ∇boldA=0.
ER -