Gradient pseudo-Ricci solitons of real hypersurfaces

Mayuko Kon

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arXiv · 2110.09739

Gradient pseudo-Ricci solitons of real hypersurfaces

Mayuko Kon

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Abstract

Let $M$ be a real hypersurface of a complex space form $M^n(c)$, $c\neq 0$. Suppose that the structure vector field $\xi$ of $M$ is an eigen vector field of the Ricci tensor $S$, $S\xi=\beta\xi$, $\beta$ being a function. We study on $M$, a gradient pseudo-Ricci soliton as an extended concept of Ricci soliton, closely related to pseudo-Einstein real hypersurfaces. We show that a $3$-dimensional ruled real hypersurface of $M^2(c), c<0$ admits a non-trivial gradient pseudo-Ricci soliton.

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BibTeX RIS

Mayuko Kon. 2021-10-19. Gradient pseudo-Ricci solitons of real hypersurfaces. https://arxiv.org/abs/2110.09739

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