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

Altay, Sezgin; Özen, Füsun

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].

Reviewer: Vladislav V. Goldberg (Newark)

MSC:

53B25	Local submanifolds
53B20	Local Riemannian geometry

Keywords:

Riemannian manifold; hypersurface; asymptotic line; net