On Quasi-Conformally Flat Generalized Sasakian-Space Forms

Year 2022, Volume: 3 Issue: 2, 119 - 131, 28.07.2022

Ahmet Yıldız

https://doi.org/10.54974/fcmathsci.1054967

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

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