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REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH GENERALIZED TANAKA–WEBSTER 𝔇^⊥-PARALLEL SHAPE OPERATOR

IMSOON JEONG

Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea

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HYUNJIN LEE

Graduate School of Electrical Engineering and Computer Science, Kyungpook National University, Taegu 702-701, Korea

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, and

YOUNG JIN SUH

Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea

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https://doi.org/10.1142/S0219887812500326Cited by:4 (Source: Crossref)

Abstract

In a paper due to [I. Jeong, H. Lee and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster parallel shape operator, Kodai Math. J.34 (2011) 352–366] we have shown that there does not exist a hypersurface in G₂(ℂ^m+2) with parallel shape operator in the generalized Tanaka–Webster connection (see [N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan J. Math.20 (1976) 131–190; S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc.314(1) (1989) 349–379]). In this paper, we introduce a new notion of generalized Tanaka–Webster 𝔇^⊥-parallel for a hypersurface M in G₂(ℂ^m+2), and give a characterization for a tube around a totally geodesic ℍ Pⁿ in G₂(ℂ^m+2) where m = 2n.

Keywords:

AMSC: Primary 53C40, Secondary 53C15

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