Tohoku Mathematical Journal

Ricci solitons and real hypersurfaces in a complex space form

Jong Taek Cho and Makoto Kimura

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Abstract

We prove that a real hypersurface in a non-flat complex space form does not admit a Ricci soliton whose potential vector field is the Reeb vector field. Moreover, we classify a real hypersurface admitting so-called “$\eta$-Ricci soliton” in a non-flat complex space form.

Article information

Source
Tohoku Math. J. (2) Volume 61, Number 2 (2009), 205-212.

Dates
First available in Project Euclid: 24 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1245849443

Digital Object Identifier
doi:10.2748/tmj/1245849443

Mathematical Reviews number (MathSciNet)
MR2541405

Zentralblatt MATH identifier
1172.53021

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Citation

Cho, Jong Taek; Kimura, Makoto. Ricci solitons and real hypersurfaces in a complex space form. Tohoku Math. J. (2) 61 (2009), no. 2, 205--212. doi:10.2748/tmj/1245849443. https://projecteuclid.org/euclid.tmj/1245849443


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