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In this paper we present a theoretical analysis of the effect of anomalies ofthe Fermi surface (FS) curvature on oscillations in the electron density ofstates (DOS) in strong magnetic fields. It is shown that the oscillations couldbe significantly strengthened when the FS curvature turns zero in thevicinities of some extremal cross sections, and they could be weakened when thecurvature takes on extremely large values or diverges there. This leads to acharacteristic dependence of the oscillations magnitude on the direction of themagnetic field which is studied. The results of these general studies areemployed to analyze the effects of the FS curvature anomalies on the quantumoscillations in the velocity of sound waves travelling in metals.Comment: 6 pages, 3 figures, text added, 1 figure adde

Local geometry of the Fermi surface and quantum oscillations in the linear response of metals