New Conditions on Normal Jacobi Operator of Real Hypersurfaces in the Complex Quadric

On a real hypersurface M of a complex quadric we have an almost contact metric structure induced by the Kählerian structure of the ambient space. Therefore, on M we have the Levi-Civita connection ∇ and, for any non-null real number k , the so called k th generalized Tanaka Webster connection ∇ ^ (...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2021-03, Vol.44 (2), p.891-903
Main Authors: Pérez, Juan de Dios, Suh, Young Jin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Hyperspaces
Mathematics
Mathematics and Statistics
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Summary:On a real hypersurface M of a complex quadric we have an almost contact metric structure induced by the Kählerian structure of the ambient space. Therefore, on M we have the Levi-Civita connection ∇ and, for any non-null real number k , the so called k th generalized Tanaka Webster connection ∇ ^ ( k ) . We introduce the notions of ( ∇ ^ ( k ) , ∇ ) -Codazzi and ( ∇ ^ ( k ) , ∇ ) -Killing normal Jacobi operator on such a real hypersurface and classify Hopf real hypersurface in a complex quadric whose normal Jacobi operators satisfy any of both conditions.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-020-00988-7