eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences August 2010 22 2 449 466 jusps-A 993 article S.S. Pujar 1 S.N. Kadlag 1 K.K. Wagh Institute of Engineering Education and Research, Panchawati, nasik - 422003 (MS) INDIA <p style="text-align: justify;">In this paper, we consider the compact, connected, orientable Riemannian manifold M of dimension n admitting a projective vector field and obtain the series of integral formulas and inequalities without assuming that the scalar curvature of M is constant . Using these integral formulas,it is obtained that the necessary and sufficient conditions for the projective vector field to be the Killing vector field. Further, if the scalar curvature of M is constant on M , then the integral formulas , inequalities and the Propositions of H. Hiramatu¹ will include as special cases from the main Lemmas and Theorems.</p> https://www.ultrascientist.org/paper/993/ Integral formulas inequalities their applications