@article{article_467824, title={Second Order Renormalization Group Flow on Warped Product Manifolds}, journal={Cankaya University Journal of Science and Engineering}, volume={16}, pages={81–97}, year={2019}, author={Razavi, Asadollah and Toeiserkani, Zoheir}, keywords={Ricci flow,second order renormalization group flow,warped product manifold}, abstract={<p>In this work we have studied the evolution of a warped product (WP) manifold under second order <br />renormalization group (RG-2) flow. We have shown some conditions for the existence of a solution of RG-2 <br />flow on WP manifolds. Also, we have found a necessary condition for warped function under RG-2 flow. In <br />particular, we study some special WP metric of real line with a manifold. Eventually, by extending conditions <br />to pseudo-Riemannian manifold, we find a PDE for Robertson-Walker (RW) metrics, and show that there is <br />no RG-2 flow for RW metrics. <br /> </p> <p> <br /> </p>}, number={1}, publisher={Cankaya University}