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I have the following basic, surely stupid, questions. Assume we have a Riemannian metric $g$ on a manifold $M$. let $a\in\mathbb{R}$ a constant and consider the metric $g_1=ag$. Which are the transformation rules for the scalar and sectional curvature and for the Ricci tensor? For the sectional I guess are the same $K_g(\pi)=K_{g_1}(\pi)$, but what about sectional and Ricci tensor. Moreover how does change the metric on tensors: is it true that $g_1(v,w)=a^{l-m}g(v,w)$ if $v,w$ are $(l,m)$-tensors? Thank you

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