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On the Structure of the Cut Locus in Certain Classes of Warped Product Manifolds
Abstract
In this paper, we determine the structure of the cut locus for a class of complete warped product manifolds M=(R1× S1,dt2+m(t)2dθ2), where the warping function m(t) is positive and even, under the assumption that there exists a positive number t1 such that the Gaussian curvature is nonpositive on the domain t−1((t1,∞) ) and is decreasing along the subarc t−1([0,t1])∩θ−1(0) of the upper half meridian.
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BibTeX
@misc{boonnam2026structure,
title = {{On the Structure of the Cut Locus in Certain Classes of Warped Product Manifolds}},
author = {Nathaphon Boonnam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15279},
eprint = {2610.15279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15279},
}
RIS
TY - UNPB
TI - On the Structure of the Cut Locus in Certain Classes of Warped Product Manifolds
AU - Nathaphon Boonnam
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15279
UR - https://arxiv.org/abs/2610.15279
AB - In this paper, we determine the structure of the cut locus for a class of complete warped product manifolds M=(R^1× S^1,dt^2+m(t)^2dθ^2), where the warping function m(t) is positive and even, under the assumption that there exists a positive number t_1 such that the Gaussian curvature is nonpositive on the domain t^−1((t_1,∞) ) and is decreasing along the subarc t^−1([0,t_1])∩θ^−1(0) of the upper half meridian.
ER -