Hopf Real Hypersurfaces in the Indefinite Complex Projective Space View Full Text


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Article Info

DATE

2019-04

AUTHORS

Makoto Kimura, Miguel Ortega

ABSTRACT

We wish to attack the problems that Anciaux and Panagiotidou posed in (Differ Geom Appl 42:1–14, 10.1016/j.difgeo.2015.05.004, 2015), for non-degenerate real hypersurfaces in indefinite complex projective space. We will slightly change these authors’ point of view, obtaining cleaner equations for the almost-contact metric structure. To make the theory meaningful, we construct new families of non-degenerate Hopf real hypersurfaces whose shape operator is diagonalisable, and one Hopf example with degenerate metric and non-diagonalisable shape operator. Next, we obtain a rigidity result. We classify those real hypersurfaces which are η-umbilical. As a consequence, we characterize some of our new examples as those whose Reeb vector field ξ is Killing. More... »

PAGES

27

References to SciGraph publications

  • 1982-03. Indefinite Kähler manifolds in MATHEMATISCHE ANNALEN
  • 2015. Geometry of Hypersurfaces in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00009-019-1299-9

    DOI

    http://dx.doi.org/10.1007/s00009-019-1299-9

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