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- Title
Hopf Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Shape Operator.
- Authors
Lee, Hyunjin; Choi, Young; Woo, Changhwa
- Abstract
In this paper, we consider a new notion of Reeb parallel shape operator for real hypersurfaces $$M$$ in complex two-plane Grassmannians $$G_2({\mathbb C}^{m+2})$$ . When $$M$$ has Reeb parallel shape operator and non-vanishing geodesic Reeb flow, it becomes a real hypersurface of Type $$(A)$$ with exactly four distinct constant principal curvatures. Moreover, if $$M$$ has vanishing geodesic Reeb flow and Reeb parallel shape operator, then $$M$$ is model space of Type $$(A)$$ with the radius $$r = \frac{\pi }{4\sqrt{2}}$$ .
- Subjects
GRASSMANN manifolds; H-spaces; HYPERSURFACES; RIEMANNIAN geometry; RIEMANNIAN manifolds
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2015, Vol 38, Issue 2, p617
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-014-0039-3