Gradient pseudo-Ricci solitons of real hypersurfaces

2021/10/19 by Mayuko Kon, Kon, Mayuko
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2110.09739

Abstract

Let M be a real hypersurface of a complex space form Mⁿ(c), c≠ 0. Suppose that the structure vector field ξ of M is an eigen vector field of the Ricci tensor S, Sξ=βξ, β 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 M²(c), c<0 admits a non-trivial gradient pseudo-Ricci soliton.

Citations

• On Ruled Real Hypersurfaces in Complex Space Forms

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