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In this study, the authors extend Manikas's array bound theory using differential geometry to direction-finding (DF) multiple-input multiple-output (MIMO) radar, and investigate the ultimate DF accuracy, detection and resolution capabilities via the manifold studies on MIMO virtual arrays. The authors derive the expression of the asymptotic normalised mean-square angular error, which is based on Cramer'Rao bounds of azimuth and elevation angles, to explore the ultimate DF accuracy both for one- and two-target cases. Furthermore, in two-target case, the authors derive the expressions of detection and resolution thresholds of directional parameters, respectively. They find that all fundamental limits above are highly dependent on the antenna geometry of DF MIMO radar systems. At last, the fundamental limits of four representative antenna geometries of DF MIMO radars, which are used in most of the current literature, are investigated and compared.