On the Gaussian curvature of maximal surfaces in n-dimensional generalized Robertson - Walker spacetimes

Details On the Gaussian curvature of maximal surfaces in n-dimensional generalized Robertson - Walker spacetimes On the Gaussian curvature of maximal surfaces in n-dimensional generalized Robertson - Walker spacetimes

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cqgra..13.3211a&link_type=abstract

Classical and Quantum Gravity, Volume 13, Issue 12, pp. 3211-3219 (1996).

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We study compact maximal surfaces in the family of generalized Robertson - Walker spacetimes. We prove an integral inequality for their Gaussian curvature K, with equality characterizing the totally geodesic case. This gives an integral alternative to the irregular behaviour of K, which is due to the fact that the normal fibre bundle is Lorentzian and that our ambient spacetimes are not necessarily spatially homogeneous. We also give some consequences and applications for certain relevant cases of these spacetimes.

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