Nets of asymptotic lines in a Riemannian hypersurface with non-symmetric metric connection. (English) Zbl 1034.53017

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 4th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6–15, 2002. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-4-1/pbk). 127-134 (2003).
Suppose that \(M^n\) be a hypersurface in a Riemannian manifold \(M^{n+1}\). A curve \(C\) on \(M^n\) is called asymptotic if the normal curvature along the curve \(C\) vanishes identically. In the paper under review the authors study the hypersurfaces \(M^n\) for which the \(n\) families of asymptotic lines form a special net (Chebyshev, geodesic, or strongly metric Chebyshev).
For the entire collection see [Zbl 1008.00022].


53B25 Local submanifolds
53B20 Local Riemannian geometry