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In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and… Click to show full abstract
In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and applies it to investigate conditions for the leaves being totally umbilical or geodesic. Using the Maximum principle with the mentioned equation we obtain an obstruction for the existence of totally geodesic spacelike foliations in a spacetime with positive Ricci curvature on the direction N .
Keywords:
lorentz manifolds;
foliations spacelike;
hypersurfaces lorentz;
spacelike hypersurfaces
Journal Title: Results in Mathematics
Year Published: 2019
Link to full text (if available)
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Journal Title: Results in Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!