Webfunctional (total scalar curvature), and to consider convexity of these functionals. They also allow us to prove rigidity theorems for certain analogues of constant curvature and Einstein manifolds in the piecewise flat setting. 1. Introduction Consider a manifold constructed by identifying the boundaries of Eu-clidean triangles or Euclidean ... WebOct 29, 2024 · If the underlying manifold is locally conformally flat (LCF), we can compute explicitly the Bochner–Weitzenböck formula for harmonic p-forms according to its Ricci …
arXiv:2304.04659v1 [math.AP] 10 Apr 2024
Webfree oriented S1-manifolds satisfying conditionC (cf. Definition 18) are oriented S1-boundaries, we get the following equivariant version of the Gromov-Lawson theorem stated above. ... then M admits an S1-invariant metric of positive scalar curvature. By Lemma 19, the manifold M satisfies condition C, if all isotropy groups have odd order. ... WebTwo manifolds with boundaries can be glued together along a boundary. If this is done the right way, the result is also a manifold. ... His theorema egregium gives a method for computing the curvature of a surface … lighting temple
MANIFOLDS OF POSITIVE SCALAR CURVATURE: A PROGRESS REPORT e ;:::;e n r …
WebMar 7, 2024 · In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold.To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial … WebarXiv:1906.04128v1 [math.DG] 10 Jun 2024 CONTRACTIBLE 3-MANIFOLDS AND POSITIVE SCALAR CURVATURE (II) JIAN WANG Abstract. In this article, we are interested in the … Webof compact Riemannian manifolds with non-negative scalar curvature: Theorem 1. (Shi-Tam) Let (;g) be an n-dimensional compact Riemann-ian spin manifold with non-negative scalar curvature and mean convex bound-ary. If every component i of the boundary is isometric to a strictly convex hypersurface ^ iˆRn, then (1) Z i Hd˙ Z ^ i Hd^ ˙^ lighting terminal block