Abstract
We prove that a four-dimensional generalized symmetric space does not admit any non-degenerate hypersurfaces with parallel second fundamental form, in particular non-degenerate totally geodesic hypersurfaces, unless it is locally symmetric. However, spaces which are known as generalized symmetric spaces of type C do admit non-degenerate parallel hypersurfaces and we verify that they are indeed symmetric. We also give a complete and explicit classification of all non-degenerate totally geodesic hypersurfaces of spaces of this type.
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This work was partially supported by project G.0432.07 of the Research Foundation–Flanders (F.W.O.).
The second author is a post-doctoral researcher supported by the Research Foundation—Flanders (F.W.O.).
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De Leo, B., Van der Veken, J. Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces. Geom Dedicata 159, 373–387 (2012). https://doi.org/10.1007/s10711-011-9665-1
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DOI: https://doi.org/10.1007/s10711-011-9665-1