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Real hypersurfaces with isometric reeb flow in complex quadrics

International Journal of Mathematics, June 2013, Vol.24(7) [Peer Reviewed Journal]

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  • Title:
    Real hypersurfaces with isometric reeb flow in complex quadrics
  • Author: Berndt, J. ; Suh, Y.J.
  • Found In: International Journal of Mathematics, June 2013, Vol.24(7) [Peer Reviewed Journal]
  • Subjects: Complex Quadric ; Real Hypersurface ; Reeb Flow
  • Rights: Copyright 2013 Elsevier B.V., All rights reserved.
  • Description: We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Q(m) = SO(m+2)/SO(m)SO(2), m (greater-than or equal to) 3. We show that m is even, say m = 2k, and any such hyper-surface is an open part of a tube around a k-dimensional complex projective space CP(k) which is embedded canonically in Q(2k) as a totally geodesic complex submanifold. As a consequence, we get the non-existence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex quadrics Q(2k+1), k (treater-than or equal to) 1. To our knowledge the odd-dimensional complex quadrics are the first examples of homogeneous Kahler manifolds which do not admit a real hypersurface with isometric Reeb flow.
  • Identifier: ISSN: 0129167X ; DOI: 10.1142/S0129167X1350050X

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