User:DemetreKaz/sandbox

I'm a phd student in mathematics new to editing math pages. $$$$

Introduction
For a smooth closed $$n$$-dimensional Riemannian manifold $$(M,g)$$ and a smooth function $$\phi\in C^\infty(M)$$, one can form the conformal metric $$\tilde{g}=\phi^{\frac{4}{n-2}}g$$. The scalar curvature of $$\tilde{g}$$ is given by


 * $$\tilde{R}=\frac{L_g\phi}{\phi^{\frac{n+2}{n-2}}}$$

where $$L_g=-\frac{4(n-1)}{n-2}\Delta_g+R_g$$ is the conformal laplacian of $$(M,g)$$.