## 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].

### MSC:

 53B25 Local submanifolds 53B20 Local Riemannian geometry

### Keywords:

Riemannian manifold; hypersurface; asymptotic line; net