Ĥ-eigenvalues of Hermitian tensors and some applications

Haojie Chen; Yang Yang

doi:10.48550/arxiv.2508.12476

August 17, 2025Open Access

Ĥ-eigenvalues of Hermitian tensors and some applications

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Key Points

H-eigenvalues are introduced for complex tensors, providing new insights into tensor properties and behaviors.
Several criteria for positive definiteness of hermitian and cps tensors are established, offering measurable validation methods.
Analysis focuses on applications in holomorphic sectional curvature, supporting richer understanding in complex differential geometry.
Results reaffirm and build upon previous findings by enhancing algebraic interpretations in tensor theory.

Implication

This work determines h-eigenvalues and inclusion sets in complex tensors, highlighting implications for differential geometry.

Abstract

We introduce Ĥ-eigenvalue for $2m$-th order n-dimensional complex tensors. Then we determine several checkable inclusion sets for Ĥ-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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Chen et al. (2025) studied this question.

synapsesocial.com/papers/68d913a34ddcf71ba560b846 https://doi.org/10.48550/arxiv.2508.12476

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Ĥ-eigenvalues of Hermitian tensors and some applications

Key Points

Implication

Abstract

Discussion

Cite This Study

Ĥ-eigenvalues of Hermitian tensors and some applications

Key Points

Implication

Abstract

Discussion

Cite This Study

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