# Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form

## Esmaeil Abedi, Reyhane Bahrami Ziabari, and Mukut Mani Tripathi

Address:

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751 71379, Iran

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751 71379, Iran

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

E-mail:

esabedi@azaruniv.edu

Bahrami.reyhane@azaruniv.edu

mmtripathi66@yahoo.com

Abstract: We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, $\theta $-slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.

AMSclassification: primary 53C40; secondary 53C25, 53D15.

Keywords: Ricci curvature, scalar curvature, squared mean curvature, conformal Sasakian space form.

DOI: 10.5817/AM2016-2-113