Note on concentration via the conjugate-linear Hodge star operator

Q: What type of study is this?

This is a Quantitative Study study.

Junho Lee

doi:10.48550/arxiv.2508.07622

August 11, 2025Open Access

Note on concentration via the conjugate-linear Hodge star operator

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Key Points

Perturbed twisted spinc Dirac operators satisfy the concentration principle, indicating a significant mathematical property of the operators.
The method involves conjugate-linear perturbations using the Hodge star operator, applied to specific dimensional almost hermitian manifolds.
Results focus on dimensions congruent to 2 or 6 modulo 8, which are critical for the mathematical implications of the study.
The research has potential implications in geometric analysis, enhancing understanding of curvature and Dirac operators.

Implication

This work demonstrates the application of conjugate-linear perturbations of twisted spinc Dirac operators, suggesting a new concentration principle.

Abstract

We construct conjugate-linear perturbations of twisted spinc Dirac operators on compact almost hermitian manifolds of dimension congruent to 2 or 6 modulo 8, employing the conjugate-linear Hodge star operator rescaled by unit complex numbers depending on degree. These perturbations satisfy the concentration principle.

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Cite This Study

Junho Lee (2025) studied this question.

synapsesocial.com/papers/68f12bfb2107091eab27a3ba https://doi.org/10.48550/arxiv.2508.07622

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