Submanifold theory and parallel transport

Franki Dillen, Johan Fastenakels, Stefan Haesen, Joeri Van der Veken, Leopold Verstraelen

A geometrical interpretation of semi-parallel submanifolds is presented in terms of parallel transport of the second fundamental form around an infinitesimal coordinate parallelogram. Further, a new scalar curvature invariant of the immersion is introduced. Isotropy of this invariant at every point means that the submanifold is pseudo-parallel.