×

Submanifold theory and parallel transport. (English) Zbl 1299.53039

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.

MSC:

53B20 Local Riemannian geometry
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
PDFBibTeX XMLCite