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Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians

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Abstract

In this paper, we introduce new notions of semi-parallel shape operators and structure Jacobi operators in complex two-plane Grassmannians \(G_2({\mathbb C}^{m+2})\). By using such a semi-parallel condition, we give a complete classification of Hopf hypersurfaces in \(G_2({\mathbb C}^{m+2})\).

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Acknowledgments

The authors would like to express their deep gratitude to Professors Y.J. Suh and J.D. Pérez for their suggestions to solve this problem and nice comments with their best effort.

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, 702-701, Republic Of Korea

    Doo Hyun Hwang, Hyunjin Lee & Changhwa Woo

Authors
  1. Doo Hyun Hwang
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  2. Hyunjin Lee
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  3. Changhwa Woo
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Corresponding author

Correspondence to Hyunjin Lee.

Additional information

Communicated by A. Constantin.

This work was supported by Grant Proj. No. NRF-2015-R1A2A1A-01002459. C. Woo is supported by NRF Grant funded by the Korean Government (NRF-2013-Fostering Core Leaders of Future Basic Science Program).

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Hwang, D.H., Lee, H. & Woo, C. Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians. Monatsh Math 177, 539–550 (2015). https://doi.org/10.1007/s00605-015-0778-8

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  • DOI: https://doi.org/10.1007/s00605-015-0778-8

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