Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14512 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910057101262848 |
|---|---|
| author | Correa, Eder M. Almeida, Lucas Wainer, Samuel |
| author_facet | Correa, Eder M. Almeida, Lucas Wainer, Samuel |
| contents | In this paper, we precisely describe the spectrum of closed invariant $(1,1)$-forms viewed as an operator acting on complex spinor bundles over rational homogeneous varieties. Using this result, we describe the spectrum of the Weitzenböck remainder of ${\rm{Spin}}^{c}$ Dirac operators on rational homogeneous varieties. In particular, we present an explicit formula for their smallest eigenvalue. As a byproduct, we obtain a new lower bound for the eigenvalues of the ${\rm{Spin}}^{c}$ Dirac operator, expressed in terms of Lie-theoretic data. Additionally, combining the Atiyah-Singer index theorem with the Borel-Weil-Bott theorem, we provide a complete classification of ${\rm{Spin}}^{c}$ structures on rational homogeneous varieties which admit harmonic spinors. In this last setting, we present an explicit formula for the index of the associated ${\rm{Spin}}^{c}$ Dirac operator in terms of Lie theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14512 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weitzenböck Remainder Spectrum on Rational Homogeneous Varieties Correa, Eder M. Almeida, Lucas Wainer, Samuel Differential Geometry In this paper, we precisely describe the spectrum of closed invariant $(1,1)$-forms viewed as an operator acting on complex spinor bundles over rational homogeneous varieties. Using this result, we describe the spectrum of the Weitzenböck remainder of ${\rm{Spin}}^{c}$ Dirac operators on rational homogeneous varieties. In particular, we present an explicit formula for their smallest eigenvalue. As a byproduct, we obtain a new lower bound for the eigenvalues of the ${\rm{Spin}}^{c}$ Dirac operator, expressed in terms of Lie-theoretic data. Additionally, combining the Atiyah-Singer index theorem with the Borel-Weil-Bott theorem, we provide a complete classification of ${\rm{Spin}}^{c}$ structures on rational homogeneous varieties which admit harmonic spinors. In this last setting, we present an explicit formula for the index of the associated ${\rm{Spin}}^{c}$ Dirac operator in terms of Lie theory. |
| title | Weitzenböck Remainder Spectrum on Rational Homogeneous Varieties |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.14512 |