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Three-dimensional noncompact trans-Sasakian η-Einstein manifolds
Abstract
We classify connected, simply connected, noncompact three-dimensional trans-Sasakian η-Einstein manifolds. In [1], we showed that, in the compact case, such a manifold is either of β-Kenmotsu type or homothetic to a Sasakian manifold. In this paper, in the noncompact case, we find families of trans-Sasakian η-Einstein manifolds that are neither β-Kenmotsu nor homothetic to Sasakian manifolds. These families have infinitely many degrees of freedom. We give these nontrivial metrics explicitly. We also give a structure theorem for the case in which the characteristic vector field is Palais-nonregular.
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BibTeX
@misc{matsuno2026threedimensional,
title = {{Three-dimensional noncompact trans-Sasakian $η$-Einstein manifolds}},
author = {Satsuki Matsuno},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39971},
eprint = {2610.39971},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39971},
}
RIS
TY - UNPB
TI - Three-dimensional noncompact trans-Sasakian η-Einstein manifolds
AU - Satsuki Matsuno
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39971
UR - https://arxiv.org/abs/2610.39971
AB - We classify connected, simply connected, noncompact three-dimensional trans-Sasakian η-Einstein manifolds. In [1], we showed that, in the compact case, such a manifold is either of β-Kenmotsu type or homothetic to a Sasakian manifold. In this paper, in the noncompact case, we find families of trans-Sasakian η-Einstein manifolds that are neither β-Kenmotsu nor homothetic to Sasakian manifolds. These families have infinitely many degrees of freedom. We give these nontrivial metrics explicitly. We also give a structure theorem for the case in which the characteristic vector field is Palais-nonregular.
ER -