PreprintCC BY 4.0arXiv
Positive mass and rigidity for asymptotically flat tangent bundles
Abstract
Let (M,g) be an asymptotically flat manifold such that its tangent bundle TM is diffeomorphically asymptotically Euclidean. We prove a positive mass theorem and a positive mass rigidity theorem for a natural class of asymptotically flat metrics g̃ on TM exhibiting slow asymptotic decay. These metrics are constructed by interpolating, along the horizontal distribution of TM, between the Euclidean metric and the base metric g near infinity. The main difficulty is that the induced metrics on TM decay below the standard threshold for the ADM mass in dimension 2n; nevertheless, we show that their asymptotic mass is well-defined in a generalized sense and is determined by geometric data on the underlying manifold M.
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BibTeX
@misc{lakzian2026positive,
title = {{Positive mass and rigidity for asymptotically flat tangent bundles}},
author = {Sajjad Lakzian},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29427},
eprint = {2608.29427},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29427},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Positive mass and rigidity for asymptotically flat tangent bundles
AU - Sajjad Lakzian
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29427
UR - https://arxiv.org/abs/2608.29427
AB - Let (M,g) be an asymptotically flat manifold such that its tangent bundle TM is diffeomorphically asymptotically Euclidean. We prove a positive mass theorem and a positive mass rigidity theorem for a natural class of asymptotically flat metrics g̃ on TM exhibiting slow asymptotic decay. These metrics are constructed by interpolating, along the horizontal distribution of TM, between the Euclidean metric and the base metric g near infinity. The main difficulty is that the induced metrics on TM decay below the standard threshold for the ADM mass in dimension 2n; nevertheless, we show that their asymptotic mass is well-defined in a generalized sense and is determined by geometric data on the underlying manifold M.
ER -