Browse > Article
http://dx.doi.org/10.4134/BKMS.2013.50.5.1567

CURVATURE OF MULTIPLY WARPED PRODUCTS WITH AN AFFINE CONNECTION  

Wang, Yong (School of Mathematics and Statistics Northeast Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1567-1586 More about this Journal
Abstract
In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifolds with constant scalar curvature. We also consider the multiply warped products with an affine connection with a zero torsion.
Keywords
multiply warped products; semi-symmetric non-metric connection; Ricci tensor; scalar curvature; Einstein manifolds;
Citations & Related Records
연도 인용수 순위
  • Reference
1 P. Ehrlich, Y. Jung, and S. Kim, Constant scalar curvatures on warped product mani-folds, Tsukuba J. Math. 20 (1996), no. 1, 239-265.   DOI
2 M. Fernandez-Lopez, E. Garcia-Rio, D. Kupeli, and B. Unal, A curvature condition for a twisted product to be a warped product, Manuscripta Math. 106 (2001), no. 2, 213-217.   DOI   ScienceOn
3 H. Hayden, Subspace of a space with torsion, Proc. Lond. Math. Soc. 34 (1932), 27-50.
4 C. Ozgur and S. Sular, Warped products with a semi-symmetric non-metric connection, Arab. J. Sci. Eng. 36 (2011), no. 3, 461-473.   DOI
5 S. Sular and C. Ozgur, Warped products with a semi-symmetric metric connection, Taiwanese J. Math. 15 (2011), no. 4, 1701-1719.   DOI
6 Y. Wang, Multiply twisted products, arXiv:1207.0199.
7 K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.
8 N. Agashe and M. Chafle, A semi-symmetric nonmetric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), 399-409.
9 N. Agashe and M. Chafle, On submanifolds of a Riemannian manifold with a semi-symmetric non-metric connection, Tensor (N.S.) 55 (1994), no. 2, 120-130.
10 L. Alias, A. Romero, and M. Sanchez, Spacelike hypersurfaces of constant mean curva-ture and Calabi-Bernstein type problems, Tohoku Math. J. (2) 49 (1997), no. 3, 337-345.   DOI
11 R. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Am. Math. Soc. 145 (1969), 1-49.   DOI
12 F. Dobarro and E. Dozo, Scalar curvature and warped products of Riemann manifolds, Trans. Amer. Math. Soc. 303 (1987), no. 1, 161-168.   DOI   ScienceOn
13 F. Dobarro and B. Unal, Curvature of multiply warped products, J. Geom. Phys. 55 (2005), no. 1, 75-106.   DOI   ScienceOn