Geodesic
Null hypersurfaces in 4-manifolds endowed with a product structure
Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 24-35

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DOI

In a 4-manifold, the composition of a Riemannian Einstein metric with an almost paracomplex structure that is isometric and parallel defines a neutral metric that is conformally flat and scalar flat. In this paper, we study hypersurfaces that are null with respect to this neutral metric, and in particular we study their geometric properties with respect to the Einstein metric. Firstly, we show that all totally geodesic null hypersurfaces are scalar flat and their existence implies that the Einstein metric in the ambient manifold must be Ricci-flat. Then, we find a necessary condition for the existence of null hypersurface with equal nontrivial principal curvatures, and finally, we give a necessary condition on the ambient scalar curvature, for the existence of null (non-minimal) hypersurfaces that are of constant mean curvature.
DOI : 10.1017/S0017089523000319
Mots-clés : almost paracomplex structures, neutral metrics, product of 2-manifolds, null hypersurfaces 
Georgiou, Nikos. Null hypersurfaces in 4-manifolds endowed with a product structure. Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 24-35. doi: 10.1017/S0017089523000319
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     title = {Null hypersurfaces in 4-manifolds endowed with a product structure},
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     year = {2024},
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