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Conjugate Frobenius Manifold and Inversion Symmetry

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Abstract

We give a conjugacy relation on certain type of Frobenius manifold structures using the theory of flat pencils of metrics. It leads to a geometric interpretation for the inversion symmetry of solutions to Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations.

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Acknowledgements

The authors thank Paolo Lorenzoni for his time to read the first draft of this article and for his suggestion to generalize the results under more general hypothesis. The authors also thank anonymous reviewers whose comments/suggestions helped clarify and improve the article. In particular, directing us to the coordinates free condition (3.1) and to the potential used in Example 3.5.

Funding

This work was partially funded by the internal grant of Sultan Qaboos University (IG/SCI/DOMS/19/08).

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Authors and Affiliations

  1. Depatment of Mathematics College of Science, Sultan Qaboos University, Muscat, Oman

    Zainab Al-Maamari & Yassir Dinar

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  1. Zainab Al-Maamari
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  2. Yassir Dinar
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Correspondence to Yassir Dinar.

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The authors have no relevant financial or non-financial interests to disclose.

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Communicated by Youjin Zhang.

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Al-Maamari, Z., Dinar, Y. Conjugate Frobenius Manifold and Inversion Symmetry. Math Phys Anal Geom 25, 23 (2022). https://doi.org/10.1007/s11040-022-09436-3

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