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

Haojie Chen; Yang Yang

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arXiv · 2508.12476

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

Haojie Chen·Yang Yang

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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.

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BibTeX RIS

Haojie Chen, Yang Yang. 2025-08-17. $\hat{H}$-eigenvalues of Hermitian tensors and some applications. https://arxiv.org/abs/2508.12476

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