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Journal of Geometry

, 109:10 | Cite as

Certain types of real hypersurfaces in complex space forms

  • Amalendu Ghosh
Article

Abstract

A nice characterization of real hypersurfaces of a nonflat complex space form is very much familiar when its structure vector field \(\xi \) is Killing. This motivates us to classify a real hypersurface of a nonflat complex space form when the structure vector field \(\xi \) is 2-Killing (i.e.,\(\pounds _{\xi }\pounds _{\xi }g = 0)\), where \(\pounds _{\xi }\) denotes the Lie derivative along the vector field \(\xi \). Further, we classify real hypersurfaces of a nonflat complex space form when the tensor field \(T (= \pounds _{\xi }g)\) is (i) weakly Lie \(\xi \)-parallel, and (ii) weakly parallel.

Keywords

Real hypersurface of complex space form 2-Killing \(\xi \)-Parallel 

Mathematics Subject Classification

53B20 53C15 53C25 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsChandernagore CollegeHooghlyIndia

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