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PreprintarXiv licencearXiv

The First Correction Term in the Asymptotic Expansion of Bohr--Sommerfeld Lagrangian States

  • Yusaku Tiba
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Abstract

Let Λ be a compact Bohr--Sommerfeld Lagrangian submanifold of a compact Kähler manifold equipped with a holomorphic prequantum line bundle. We study the asymptotic expansion of the Lagrangian states associated with Λ. In particular, we compute explicitly the first nontrivial correction term and show that it is expressed in terms of geometric invariants of the ambient Kähler manifold and the Lagrangian submanifold, including their scalar curvatures, the second fundamental form, and the mean curvature. As a consequence, we obtain the corresponding second-order asymptotic formula for the L2-norm of the Lagrangian states.

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Cite

BibTeXRIS
BibTeX
@misc{tiba2026first,
  title = {{The First Correction Term in the Asymptotic Expansion of Bohr--Sommerfeld Lagrangian States}},
  author = {Yusaku Tiba},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10909},
  eprint = {2609.10909},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10909},
}
RIS
TY  - UNPB
TI  - The First Correction Term in the Asymptotic Expansion of Bohr--Sommerfeld Lagrangian States
AU  - Yusaku Tiba
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10909
UR  - https://arxiv.org/abs/2609.10909
AB  - Let Λ be a compact Bohr--Sommerfeld Lagrangian submanifold of a compact Kähler manifold equipped with a holomorphic prequantum line bundle. We study the asymptotic expansion of the Lagrangian states associated with Λ. In particular, we compute explicitly the first nontrivial correction term and show that it is expressed in terms of geometric invariants of the ambient Kähler manifold and the Lagrangian submanifold, including their scalar curvatures, the second fundamental form, and the mean curvature. As a consequence, we obtain the corresponding second-order asymptotic formula for the L^2-norm of the Lagrangian states.
ER  -