Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]