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October 17, 20250 citationsOpen Access

Conformal Vector Fields on Damek-Ricci Space

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HSHiroyasu SatohHSHemangi Madhusudan Shah

Key Points

  • Every conformal vector field in a Damek-Ricci space is a Killing vector field, indicating special geometric constraints.
  • This finding aligns with the established theorem on complex hyperbolic spaces, broadening its applicability.
  • The research highlights the uniqueness of conformal vector fields in these geometric structures, contributing to differential geometry.
  • This work indicates that non-trivial conformal vector fields do not exist on Damek-Ricci spaces, which aids in understanding their structure.

Abstract

In this article, we show that every conformal vector field on a Damek-Ricci space is necessarily a Killing vector field; in other words, there exists no non-trivial conformal vector field on such spaces. This result generalizes the corresponding theorem for complex hyperbolic spaces established in arXiv:2506.09710.

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Cite This Study

Satoh et al. (2025) studied this question.

synapsesocial.com/papers/68f19f20de32064e504ddf13https://doi.org/10.48550/arxiv.2507.18137
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