Examinando por Materia "Totally geodesic surfaces"

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    Totally geodesic surfaces and the Hopf's conjecture.
    (2011-10-13) Perdomo, Oscar
    Let g be a riemannian metric on [S.sup.2] x [S.sup.2]. In this paper we will show that if ([S.sup.2] x [S.sup.2], g) contains a totally geodesic torus, then [S.sup.2] x [S.sup.2] does not have positive sectional curvature. Then, we use the formula for the second variation of energy to rule out a family of metrics from having positive sectional curvature.