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Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II

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Abstract

Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces M of Type (A) in complex two plane Grassmannians G 2(ℂm+2) with a commuting condition between the shape operator A and the structure tensors φ and φ 1 for M in G 2(ℂm+2). Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator A and a new operator φφ 1 induced by two structure tensors φ and φ 1. That is, this commuting shape operator is given by φφ 1 A = A φφ 1. Using this condition, we prove that M is locally congruent to a tube of radius r over a totally geodesic G 2(ℂm+1) in G 2(ℂm+2).

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Authors and Affiliations

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

    Hyunjin Lee, Seonhui Kim & Young Jin Suh

Authors
  1. Hyunjin Lee
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  2. Seonhui Kim
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  3. Young Jin Suh
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Corresponding author

Correspondence to Hyunjin Lee.

Additional information

This work was supported by grant Proj. No. NRF-2011-220-C00002 from National Research Foundation of Korea. The first author was supported by grant Proj. No. NRF-2012R1A1A3002031 and the third by grant Proj. No. NRF-2012R1A2A2A01043023.

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Lee, H., Kim, S. & Suh, Y.J. Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II. Czech Math J 64, 133–148 (2014). https://doi.org/10.1007/s10587-014-0089-6

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  • DOI: https://doi.org/10.1007/s10587-014-0089-6

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