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PreprintarXiv licencearXiv

A Smooth Counterexample to the Trautman Conjecture

  • Sean N. Curry
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Abstract

The Trautman conjecture asserted that a smooth three-dimensional CR manifold admitting a nowhere-zero closed section of its canonical bundle must be locally embeddable in ℂ2. We modify a standard construction of nonembeddable smooth strongly pseudoconvex CR 3-manifolds so that the condition of having a nowhere-zero closed section of the canonical bundle is preserved, thus providing a strongly pseudoconvex counterexample to the Trautman conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{curry2026smooth,
  title = {{A Smooth Counterexample to the Trautman Conjecture}},
  author = {Sean N. Curry},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03198},
  eprint = {2609.03198},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03198},
}
RIS
TY  - UNPB
TI  - A Smooth Counterexample to the Trautman Conjecture
AU  - Sean N. Curry
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03198
UR  - https://arxiv.org/abs/2609.03198
AB  - The Trautman conjecture asserted that a smooth three-dimensional CR manifold admitting a nowhere-zero closed section of its canonical bundle must be locally embeddable in ℂ^2. We modify a standard construction of nonembeddable smooth strongly pseudoconvex CR 3-manifolds so that the condition of having a nowhere-zero closed section of the canonical bundle is preserved, thus providing a strongly pseudoconvex counterexample to the Trautman conjecture.
ER  -