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Zbl 1032.53004
Özen, Füzun; Altay, Sezgin
Conformal mappings and special networks of Weyl spaces.
(English)
[A] Mladenov, Iva\" ilo 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. 239-247 (2003). ISBN 954-90618-4-1/pbk

The authors prove the following theorems:\par Theorem 1. If \$W_n\$ is a totally umbilical hypersurface of a recurrent Weyl space \$W_{n+1}\$, then \$W_n\$ is also conformally recurrent.\par Theorem 2. Let a totally umbilical hypersurface \$W_n\$ of a recurrent Weyl space \$W_{n+1}\$ be conharmonically Ricci-recurrent \$(n>2)\$. If any net \$(v_1,v_2,\dots, v_n)\$ in \$W_n\$ is a Chebyshev net of first kind with respect to \$W_{n+1}\$, it is also a Chebyshev net of the first kind with respect to \$W_n\$ and the converse is also true.\par Theorem 3. Let a totally umbilical hypersurface \$W_n\$ of a recurrent Weyl space \$W_{n+1}\$ be conharmonically Ricci-recurrent \$(n> 2)\$. If any net \$(v_1,v_2,\dots, v_n)\$ in \$W_n\$ is a Chebyshev net of the second kind with respect to \$W_{n+1}\$, it is also a Chebyshev net of the second kind with respect to \$W_n\$ and the converse is also true.\par Theorem 4. Let a totally umbilical hypersurface \$W_n\$ of a recurrent Weyl space \$W_{n+1}\$ be conharmonically Ricci-recurrent \$(n> 2)\$. If any net \$(v_1,v_2,\dots, v_n)\$ in \$W_n\$ is a geodesic net with respect to \$W_{n+1}\$ it is also a geodesic net with respect to \$W_n\$ and conversely.
[A.Neagu (Iaşi)]
MSC 2000:
*53B15 Other connections
53C40 Submanifolds (differential geometry)

Keywords: recurrent Weyl space; Weyl connection; affine deformation tensor; umbilical hypersurface; conharmonic transformation

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