Dillen, Franki; Fastenakels, Johan; Haesen, Stefan; Van der Veken, Joeri; Verstraelen, Leopold Submanifold theory and parallel transport. (English) Zbl 1299.53039 Kragujevac J. Math. 37, No. 1, 33-43 (2013). Summary: 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. Cited in 3 Documents MSC: 53B20 Local Riemannian geometry 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:submanifolds; semi-parallel; pseudo-parallel PDFBibTeX XMLCite \textit{F. Dillen} et al., Kragujevac J. Math. 37, No. 1, 33--43 (2013; Zbl 1299.53039)