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Real Hypersurfaces in Complex Two-plane Grassmannians with \({\mathfrak{D}^{\bot}}\)-Parallel Shape Operator

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Abstract

In this paper we consider a new notion of \({\mathfrak{D}^{\bot}}\)-parallel shape operator for real hypersurfaces in complex two-plane Grassmannians \({G_2(\mathbb{C}^{m+2})}\) and give a non-existence theorem for a Hopf hypersurface in \({G_2(\mathbb{C}^{m+2})}\) with \({\mathfrak{D}^{\bot}}\)-parallel shape operator.

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Authors and Affiliations

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

    Imsoon Jeong, Hyunjin Lee & Young Jin Suh

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  1. Imsoon Jeong
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  2. Hyunjin Lee
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  3. Young Jin Suh
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Corresponding author

Correspondence to Young Jin Suh.

Additional information

This work was supported by Grant Proj. No. NRF-2011-220-C00002 from National Research Foundation of Korea. I. Jeong by Grant Proj. No. NRF-2011-0013381, H. Lee by Grant Proj. No. NRF-2012-R1A1A3002031, and Y. J. Suh by Grant Proj. No. NRF-2012-R1A2A2A01043023.

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Jeong, I., Lee, H. & Suh, Y.J. Real Hypersurfaces in Complex Two-plane Grassmannians with \({\mathfrak{D}^{\bot}}\)-Parallel Shape Operator. Results. Math. 64, 331–342 (2013). https://doi.org/10.1007/s00025-013-0317-7

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  • DOI: https://doi.org/10.1007/s00025-013-0317-7

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