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In this paper, we investigate a class of quadratic Riemannian curvature functionals on closed smooth manifold $M$ of dimension $nge 3$ on the space of Riemannian metrics on $M$ with unit volume. We study the stability of these functionals at the metric with constant sectional curvature as its critical point.
In this article we continue the study of the two curvature notions for Kahler manifolds introduced by the first named author earlier: the so-called cross quadratic bisectional curvature (CQB) and its dual ($^d$CQB). We first show that compact Kahler
We provide a general Bochner type formula which enables us to prove some rigidity results for $V$-static spaces. In particular, we show that an $n$-dimensional positive static triple with connected boundary and positive scalar curvature must be isome
Consider a Riemannian manifold $(M^{m}, g)$ whose volume is the same as the standard sphere $(S^{m}, g_{round})$. If $p>frac{m}{2}$ and $int_{M} left{ Rc-(m-1)gright}_{-}^{p} dv$ is sufficiently small, we show that the normalized Ricci flow initiated
We examine relations between geometry and the associated curvature decompositions in Weyl geometry.
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions are required on the functionals.