RICCI-BOURGUIGNON AND GRADIENT SOLITONS ON REAL HYPERSURFACES IN THE COMPLEX QUADRIC

Hyunjin LEE; Eunmi PAK; Young Jin SUH

doi:10.2206/kyushujm.77.331

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

RICCI-BOURGUIGNON AND GRADIENT SOLITONS ON REAL HYPERSURFACES IN THE COMPLEX QUADRIC

Hyunjin LEE, Eunmi PAK, Young Jin SUH

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Keywords: Ricci soliton, Ricci-Bourguignon soliton, generalized pseudo-anti-commuting property, 𝔄-isotropic, 𝔄-principal, complex conjugation, complex quadric

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2023 Volume 77 Issue 2 Pages 331-354

DOI https://doi.org/10.2206/kyushujm.77.331

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Abstract

By using the property of generalized pseudo-anti-commuting, Ric Φ + Φ Ric = f Φ, for real hypersurfaces in the complex quadric Q^m = SO_m+₂/SO₂SO_m, we give a complete classification of Ricci-Bourguignon soliton Hopf real hypersurfaces in the complex quadric Q^m. Then, as an application, we show a complete classification of Hopf Ricci-Bourguignon gradient solitons in the complex quadric Q^m.

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