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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.12476 |
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| _version_ | 1866911109429067776 |
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| author | Chen, Haojie Yang, Yang |
| author_facet | Chen, Haojie Yang, Yang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\hat{H}$-eigenvalues of Hermitian tensors and some applications Chen, Haojie Yang, Yang Spectral Theory Differential Geometry 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. |
| title | $\hat{H}$-eigenvalues of Hermitian tensors and some applications |
| topic | Spectral Theory Differential Geometry |
| url | https://arxiv.org/abs/2508.12476 |