Abstract
Schouten tensor, which is expressed by the Ricci curvature and scalar curvature is a Codazzi tensor on a Riemannian manifold M(dimM>3)with harmonic Weyl conformal curvature tensor. By using this tensor, an operator r can be induced, which is self-adjoint relative to the L2 - inner product. Using this operator, some equalities and inequalities are obtained. Then by equalities between certain function on a compact local conformally symmetric Riemannie manifold, Einstein manifold and constant sectional curvature space are characterized. Some new theorems are established.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Hertrich-Jeromin, U.: Models in Meobius Differential Geometry, pp.16–22 (2001)
Okumura, M.: Hypersurfaces and a pinching problem on the second fundamental tensor. Amer. J. Math., 207–213 (1974)
Cheng, S.Y., Yau, S.T.: Hypersurfaces with constant scalar curvature. Math. Ann., 195–204 (1977)
Chern, S.S., Do Carmo, M., Kobayashi, S.: Minimal submanifold of a sphere with second fundamentalform of constant length. In: Browder, F.E. (ed.) Fuctional Analysis and Related Fields, pp. 59–75. Springer, New York (1970)
Li, H.: Hypersurface with constant scalar curvature in space forms. Math. Ann., 665–672 (1996)
Yau, S.T.: Lectures on Differential Geometry, pp. 231–250. Higher Education Press (2004)
Baek, J.O., Suh, Y.J.: KYUNGPOOK Math. J. 44 Conformally Recurrent Riemannian Manifolds with Harmonic Conformal Curvature Tensor, 47–61 (2004)
Malek, F., Samavaki, M.: On weakly symmetric Riemannian manifolds. Differential Geometry - Dynamical Systems 10, 215–220 (2008)
Stanis law Ewert-Krzemieniewski, Conformally Flat Totally Umbilical Submanifolds in Some Semi-Riemannian Manifolds, KYUNGPOOK Math. J. 48,183-194 (2008)
Murathana, C., O zgur̈, C.: Riemannian manifolds with a semi-symmetric metric connection satisfying some semisymmetry conditions. In: Proceedings of the Estonian Academy of Sciences, pp. 210–216 (2008)
Nan, J., Xinghua, M., Yunwei, X., Yamian, P.: Conformal Flat Manifold and A Pinching Problem on the Schouten Tensor. In: DCABES 2009 Proceedings, pp. 99–100 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ji, N., Luo, Y., Yan, Y. (2010). Applications of Schouten Tensor on Conformally Symmetric Riemannie Manifold. In: Zhu, R., Zhang, Y., Liu, B., Liu, C. (eds) Information Computing and Applications. ICICA 2010. Communications in Computer and Information Science, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16336-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-16336-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16335-7
Online ISBN: 978-3-642-16336-4
eBook Packages: Computer ScienceComputer Science (R0)