PreprintCC BY 4.0arXiv
Positive scalar curvature on products of noncompact manifolds
Abstract
We prove that the product of three connected noncompact smooth manifolds without boundary admits a complete metric of uniformly positive scalar curvature. The proof uses the additivity of Morse indices on products and an orientation-free version of Das's open Morse--surgery construction. We also give an example of two open manifolds whose product admits no complete metric of nonnegative scalar curvature.
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BibTeX
@misc{chen2026positive,
title = {{Positive scalar curvature on products of noncompact manifolds}},
author = {Lizhi Chen and Kuntao Jin and Milan Jovanovic},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30685},
eprint = {2609.30685},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30685},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Positive scalar curvature on products of noncompact manifolds
AU - Lizhi Chen
AU - Kuntao Jin
AU - Milan Jovanovic
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30685
UR - https://arxiv.org/abs/2609.30685
AB - We prove that the product of three connected noncompact smooth manifolds without boundary admits a complete metric of uniformly positive scalar curvature. The proof uses the additivity of Morse indices on products and an orientation-free version of Das's open Morse--surgery construction. We also give an example of two open manifolds whose product admits no complete metric of nonnegative scalar curvature.
ER -