Geodesic
On semi-Riemannian manifolds satisfying some conformally invariant curvature condition
Ryszard Deszcz 1   ; Małgorzata Głogowska 1   ; Hideko Hashiguchi 2   ; Marian Hotloś 3   ; Makoto Yawata 2
1 Department of Mathematics Wrocław University of Environmental and Life Sciences Grunwaldzka 53 50-357 Wrocław, Poland
2 Department of Mathematics Chiba Institute of Technology Shibazono Narashino 275-0023, Chiba, Japan
3 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Colloquium Mathematicum, Tome 131 (2013) no. 2, pp. 149-170 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We investigate semi-Riemannian manifolds with pseudosymmetric Weyl curvature tensor satisfying some additional condition imposed on their curvature tensor. Among other things we prove that the so-called Roter type equation holds on such manifolds. We present applications of our results to hypersurfaces in semi-Riemannian space forms, as well as to $4$-dimensional warped products.
DOI : 10.4064/cm131-2-1
Keywords: investigate semi riemannian manifolds pseudosymmetric weyl curvature tensor satisfying additional condition imposed their curvature tensor among other things prove so called roter type equation holds manifolds present applications results hypersurfaces semi riemannian space forms dimensional warped products

Ryszard Deszcz  1   ; Małgorzata Głogowska  1   ; Hideko Hashiguchi  2   ; Marian Hotloś  3   ; Makoto Yawata  2

1 Department of Mathematics Wrocław University of Environmental and Life Sciences Grunwaldzka 53 50-357 Wrocław, Poland
2 Department of Mathematics Chiba Institute of Technology Shibazono Narashino 275-0023, Chiba, Japan
3 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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     title = {On {semi-Riemannian} manifolds satisfying some conformally invariant curvature condition},
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Ryszard Deszcz; Małgorzata Głogowska; Hideko Hashiguchi; Marian Hotloś; Makoto Yawata. On semi-Riemannian manifolds satisfying some conformally invariant curvature condition. Colloquium Mathematicum, Tome 131 (2013) no. 2, pp. 149-170. doi: 10.4064/cm131-2-1

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