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PreprintarXiv licencearXiv

Constant kth-mixed curvature on locally conformal Kähler manifolds

  • Kai Tang
  • Zuocai Wang
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Abstract

In this paper, we consider compact locally conformal Kähler manifolds with constant kth-mixed curvature. By using a recent method of Huang-Wan for constant Chern holomorphic sectional curvature, we prove that if a compact LCK manifold has nonzero constant kth-mixed curvature, then its Hermitian metric is Kähler. For the second mixed curvature, the same conclusion also holds when the curvature constant is zero. We also study some special parameters related to the general constant mixed curvature conjecture. In particular, we obtain a torsion-energy identity and a sign obstruction for compact Hermitian manifolds, and characterize an exceptional Kähler case by Bochner--Kähler geometry.

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Cite

BibTeXRIS
BibTeX
@misc{tang2026constant,
  title = {{Constant $k$th-mixed curvature on locally conformal Kähler manifolds}},
  author = {Kai Tang and Zuocai Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05852},
  eprint = {2609.05852},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05852},
}
RIS
TY  - UNPB
TI  - Constant kth-mixed curvature on locally conformal Kähler manifolds
AU  - Kai Tang
AU  - Zuocai Wang
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05852
UR  - https://arxiv.org/abs/2609.05852
AB  - In this paper, we consider compact locally conformal Kähler manifolds with constant kth-mixed curvature. By using a recent method of Huang-Wan for constant Chern holomorphic sectional curvature, we prove that if a compact LCK manifold has nonzero constant kth-mixed curvature, then its Hermitian metric is Kähler. For the second mixed curvature, the same conclusion also holds when the curvature constant is zero. We also study some special parameters related to the general constant mixed curvature conjecture. In particular, we obtain a torsion-energy identity and a sign obstruction for compact Hermitian manifolds, and characterize an exceptional Kähler case by Bochner--Kähler geometry.
ER  -