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Harmonic Forms and Generalized Solitons

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Abstract

In this article we study some geometric properties of generalized solitons. In particular, we establish certain relations between harmonicity and generalized solitons. For a generalized soliton \((g,\xi ,\eta ,\beta ,\gamma ,\delta )\) we derive the necessary and sufficient conditions for the dual 1-form \(\xi ^{\flat }\) of the potential field \(\xi \) to be a solution of the Schrödinger–Ricci equation, a harmonic or a Schrödinger–Ricci harmonic form. Also, we characterize the 1-forms which are orthogonal to \(\xi ^{\flat }\) for the Ricci and Yamabe solitons. Moreover, we formulate the corresponding results for gradient generalized solitons. Several applications and examples are also presented in this article.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, 300223, Timişoara, Romania

    Adara M. Blaga

  2. Department of Mathematics, Michigan State University, East Lansing, Michigan, 48824-1027, USA

    Bang-Yen Chen

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  1. Adara M. Blaga
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  2. Bang-Yen Chen
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Correspondence to Adara M. Blaga.

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Blaga, A.M., Chen, BY. Harmonic Forms and Generalized Solitons. Results Math 79, 16 (2024). https://doi.org/10.1007/s00025-023-02041-y

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