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arXiv · 2107.04223

Harmonic forms and generalized solitons

Adara M. Blaga·Bang-Yen Chen
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Abstract

For a generalized soliton $(g,\xi,\eta,\beta,\gamma,\delta)$, we provide necessary and sufficient conditions for the dual $1$-form $\xi^{\flat}$ of the potential vector field $\xi$ to be a solution of the Schr\"{o}dinger-Ricci equation, a harmonic or a Schr\"{o}dinger-Ricci harmonic form. We also characterize the $1$-forms orthogonal to $\xi^{\flat}$, underlying the results obtained for the Ricci and Yamabe solitons. Further, we formulate the results for the case of gradient generalized solitons. Several applications and examples are also presented.

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BibTeXRIS

Adara M. Blaga, Bang-Yen Chen. 2021-07-09. Harmonic forms and generalized solitons. https://doi.org/10.1007/s00025-023-02041-y

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