On Quasi-Conformally Flat Generalized Sasakian-Space Forms

Abstract

In this paper, we classify quasi-conformally flat generalized Sasakian-space forms under the assumption that the characteristic vector field is Killing. Also we classify quasi-conformally Weyl-symmetric generalized Sasakian-space forms.

Keywords

• Generalized Sasakian-space forms
• quasi-conformally ‡at
• quasiconformally Weyl-symmetric.

References

1. Alegre P., Blair D., Carriazo A., Generalized Sasakian-space forms, Israel Journal of Mathematics, 141, 157-183, 2004.
2. Blair D., Riemannian Geometry of Contact and Sympletic Manifolds, Birkhauser, 2002.
3. Derdzinski A., Some remarks on the local structure of Codazzi tensors, Lecture Notes in Mathematics, 838, 251-255, 1981.
4. Derdzinski A., Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor, Mathematische Zeitschrift, 172, 273-280, 1980.
5. Kim U.K., Conformally flat generalized Sasakian-space forms and locally symmetric generalized Sasakian space-forms, Note di Matematica, 26, 55-67, 2006.
6. Ludden G., Submanifolds of cosymplectic manifolds, Journal of Differential Geometry, 4, 237-244, 1970.
7. Sarkar A., De U.C., Some curvature properties of generalized Sasakian-space forms, Lobashevskii Journal of Mathematics, 33, 22-27, 2012.
8. Yano K., Sawaki S., Riemannian manifolds admitting a conformal transformation group, Journal of Differential Geometry, 2, 161-184, 1968.