In this paper we present a local description for complete minimal hypersurfaces in S 5 with zero Gauss-Kronecker curvature, zero 3mean curvature and nowhere zero second fundamental form.Mathematics Subject Classification (2010). 53C42.

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This work explores the scalar and Dirac quasinormal modes pertaining to a class of black hole solutions in the scalar-tensor-Gauss-Bonnet theory. The black hole metrics in question are novel analytic solutions recently derived in the extended version of the latter theory, which effectively follows at the level of the action of string theory. Owing to the existence of a nonlinear electromagnetic field, the black hole solution possesses a nonvanishing magnetic charge. In particular, the metric is capable of describing black holes with distinct characteristics by assuming different values of the ADM mass and the magnetic charge. The present study is devoted to investigating the scalar and Dirac perturbations in the above black hole spacetimes, and in particular, based on distinct horizon structures, we focus on two different types of solutions. The properties of the complex frequencies of the obtained dissipative oscillations are investigated, and subsequently, the stability of the metric is addressed. We elaborate on the possible implications of the present study.

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Дано локальное описание полных минимальных гиперповерхностей в $\mathbb{S}^5$ с нулевой кривизной Гаусса-Кронекера, нулевой $3$-средней кривизной и нигде не обращающейся в нуль второй квадратичной формой. Библиография: 16 наименований.