Abstract
Using GTW connection, we considered a real hypersurface M in a complex two-plane Grassmannian \({G_{2}({\mathbb{C}}^{m+2})}\) when the GTW Reeb Lie derivative of the structure Jacobi operator coincides with the Reeb Lie derivative. Next using the method of simultaneous diagonalization, we prove a complete classification for a real hypersurface in \({G_{2}({\mathbb{C}}^{m+2})}\) satisfying such a condition. In this case, we have proved that M is an open part of a tube around a totally geodesic \({G_{2}({\mathbb{C}}^{m+1})}\) in \({G_{2}({\mathbb{C}}^{m+2})}\).
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This work was supported by Grant Proj. No. NRP-2012-R1A2A2A-01043023.
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Pak, E., Kim, G.J. & Suh, Y.J. Real Hypersurfaces in Complex Two-Plane Grassmannians with GTW Reeb Lie Derivative Structure Jacobi Operator. Mediterr. J. Math. 13, 1263–1272 (2016). https://doi.org/10.1007/s00009-015-0535-1
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DOI: https://doi.org/10.1007/s00009-015-0535-1