Semi-Riemannian hypersurfaces in manifolds with metric mixed 3-structures
The mixed 3-structures are the counterpart of paraquaternionic structures in odd dimension. A compatible metric with a mixed 3-structure is necessarily semi-Riemann and mixed 3-Sasakian manifolds are Einstein. We investigate the differential geometry of the semi-Riemannian hypersurfaces of co-index both 0 and 1 in a manifold endowed with a mixed 3-structure and a compatible metric.
Key words and phrasesnon-degenerate hypersurface mixed 3-structure Einstein manifold
2000 Mathematics Subject Classification53C15 53C50 53C40 53C12
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- D. V. Alekseevsky, V. Cortes, A. S. Galaev and T. Leistner, Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math. (2009), in press.Google Scholar
- A. Bejancu and H. R. Farran, Foliations and Geometric Structures, Mathematics and Its Applications (Springer, 2006).Google Scholar
- D. E. Blair, Contact Manifolds in Riemannian Geometry, Lectures Notes in Math. 509 (Springer-Verlag, 1976).Google Scholar
- S. Ianuş, M. Visinescu and G. E. Vîlcu, Conformal Killing-Yano tensors on manifolds with mixed 3-structures, SIGMA, Symmetry Integrability Geom. Methods Appl., 5 (2009), Paper 022, 12 pp.Google Scholar