Harmonic forms and generalized solitons

Abstract

For a generalized soliton $(g,\xi ,\eta ,\beta ,\gamma ,\delta )$, we provide necessary and sufficient conditions for the dual $1$-form ${\xi }^{♭}$ of the potential vector field $\xi$ to be a solution of the Schrödinger-Ricci equation, a harmonic or a Schrödinger-Ricci harmonic form. We also characterize the $1$-forms orthogonal to ${\xi }^{♭}$, 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.

20 pages

References in corpus (1)

• Euclidean submanifolds with incompressible canonical vector field