Four metrics

Four-manifolds without Einstein Metrics

It is shown that there are infinitely many compact simply connected smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2χ > 3|τ |. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.

Einstein Metrics , Four - Manifolds , and Differential Topology

where r is the Ricci tensor of g and λ is some real constant [7]. We still do not know if there are any obstructions to the existence of Einstein metrics on highdimensional manifolds, but it has now been known for three decades that not every 4-manifold admits such metrics [20, 37]. Only recently, however, has it emerged that there are also obstructions to the existence of Einstein metrics whic...

Four Quantitative Metrics Describing Narrative Conflict

Conflict is an essential element of interesting stories. In previous work, we proposed a formal model of narrative conflict along with 4 quantitative dimensions which can be used to distinguish one conflict from another based on context: balance, directness, intensity, and resolution. This paper presents the results of an experiment designed to measure how well these metrics predict the respons...

Explorer Four Metrics to Evaluate Heterogeneous Multicores

Four-dimensional Osserman Metrics of Neutral Signature

In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jordan Osserman if and only if either it has constant sectional curvature or it...