$\hat{H}$-eigenvalues of Hermitian tensors and some applications

Haojie Chen; Yang Yang

$\hat{H}$-eigenvalues of Hermitian tensors and some applications

Spectral Theory 2025-08-19 v1 Differential Geometry

Authors: Haojie Chen , Yang Yang

Abstract

We introduce $\hat{H}$ -eigenvalue for $2m$ -th order $n$ -dimensional complex tensors. Then we determine several checkable inclusion sets for $\hat{H}$ -eigenvalues and derive some criterions for the Hermitian positive definiteness (semi-definiteness) of Hermitian and CPS tensors. We also apply the Hermitian tensors to study holomorphic sectional curvature in complex differential geometry and reprove the algebraic part of recent results by Alvarez-Heier-Zheng and Chaturvedi-Heier.

Keywords

Hermitian tensor $\hat{H}$-eigenvalue positive definiteness holomorphic sectional curvature complex differential geometry

Cite

@article{arxiv.2508.12476,
  title  = {$\hat{H}$-eigenvalues of Hermitian tensors and some applications},
  author = {Haojie Chen and Yang Yang},
  journal= {arXiv preprint arXiv:2508.12476},
  year   = {2025}
}

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19 pages

$\hat{H}$-eigenvalues of Hermitian tensors and some applications

Abstract

Keywords

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