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).

##### MSC:

53B25 | Local submanifolds |

53B20 | Local Riemannian geometry |