Related papers: Weyl structures with positive Ricci tensor

For the Bach-flat closed manifold with positive scalar curvature, we prove a rigidity result under a given inequality involving the Weyl curvature and the traceless Ricci curvature. Moveover, under an inequality involving…

In this paper we use the Weitzenb\"ock formulas to get information about the Betti numbers of compact nearly $G_2$ and compact nearly K\"{a}hler $6$-manifolds. First, we establish estimates on two curvature-type self adjoint operators on…

We consider Lorentzian manifolds with parallel light-like vector field V. Being parallel and light-like, the orthogonal complement of V induces a codimension one foliation. Assuming compactness of the leaves and non-negative Ricci curvature…

We prove pinching estimates for solutions of the linearized Ricci flow system on a closed manifold of dimension $n\geq 4$ with positive scalar curvature and vanishing Weyl tensor. If the vanishing Weyl tensor condition is removed, we only…

We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence…

We show that any compact half-conformally flat manifold of negative type, with bounded $L^2$ energy, sufficiently small scalar curvature, and a non-collapsing assumption, has all betti numbers bounded. We show that this result is optimal…

We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a congruence hyperbolic 3--orbifold asymptotically vanishes…

A linear constraint is given on the Betti numbers of a compact hyper-Kaehler manifold, using an index formula for c_1c_{n-1} on an almost complex manifold. The topology of some other manifolds with reduced holonomy is also discussed…

Let N be a symmetric space of dimension n > 5 whose de Rham decomposition contains no factors of constant curvature and let W be the Weyl tensor of N at some point. We prove that a Riemannian manifold whose Weyl tensor at every point is a…

We show that every Vaisman manifold with large first Betti number and vanishing first basic Chern class is diffeomorphic to a Kodaira-Thurston manifold. Furthermore, its complex structure is left-invariant, the characteristic foliation is…

We prove vanishing results for the coherent cohomology of the good reduction modulo $p$ of the Siegel variety with coefficients in some automorphic bundles. We show that for an automorphic bundle with highest weight $\lambda$ near the walls…

We introduce a general algebraic decomposition of Riemann-like and Weyl-like tensors with respect to a non-null vector $u$. We derive Gauss, Codazzi and Ricci-type identities for the Weyl tensor, that allow to relate the components of the…

We shall prove a new non-vanishing theorem for the stable cohomotopy Seiberg-Witten invariant of connected sums of 4-manifolds with positive first Betti number. The non-vanishing theorem enables us to find many new examples of 4-manifolds…

We explore connections between geometrical properties of null congruences and the algebraic structure of the Weyl tensor in n>4 spacetime dimensions. First, we present the full set of Ricci identities on a suitable "null" frame, thus…

A significant theorem of L\"uck says that the first $L^2$-Betti number of the total space of a fibration vanishes under some conditions on the fundamental groups. The proof is based on constructions on chain complexes. In the present paper,…

We find necessary and sufficient conditions for a Riemannian four-dimensional manifold $(M, g)$ with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and…

We show that compact, $n$-dimensional Riemannian manifolds with $\frac{n+2}{2}$-nonnegative curvature operators of the second kind are either rational homology spheres or flat. More generally, we obtain vanishing of the $p$-th Betti number…

A Cohen-Macaulay local ring $R$ satisfies trivial vanishing if $\operatorname{Tor}_i^R(M,N)=0$ for all large $i$ implies $M$ or $N$ has finite projective dimension. If $R$ satisfies trivial vanishing then we also have that…

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations,…

The Colding-Gromov gap theorem asserts that an almost non-negatively Ricci curved manifold with unit diameter and maximal first Betti number is homeomorphic to the flat torus. In this paper, we prove a parametrized version of this theorem,…