The geodesie curvature for an analytic complex curve, as formally defined by Schouten and van Dantzig, is shown substantially to coincide with the notion of curvature for the invariant surfaces of a kählerian manifold, geometrically defined by Martinelli.
Every compact Lie group of dimension is shown to be the bord of a G-variety; in consequence of that, every principal fibre bundle having G as structural group and a variety without boundary as base is shown to be a bord as well.
A theorem of F. Severi giving a geodesie construction of Levi-Civita’s parallelism is extended in the range of the linear connections with arbitrary torsion. Applications to totally geodesic submanifolds and to almost complex manifolds are given.
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