In this paper, we classify 3-dimensional complete self-shrinkers in Euclidean space \({\mathbb {R}}^{4}\) with constant squared norm of the second fundamental form S and \(f_{4}\).

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .

We demonstrate that random walks embed connected undirected graphs into Euclidean space, in which distances and angles acquire the clear statistical interpretation. Being defined on the spatial network of Venetian canals, random walks afford a portrait of the city space syntax and measure its intelligibility. In the present Letter, we investigate the spatial network of 96 canals in Venice (that...

The observables of supergravity are defined to be the phase space gauge invariant objects of the theory. Dirac eigenvalues are obsevables of Euclidean gravity on a compact manifold [1,2,3]. We resume the basic results for super-gravity [4,5], [6,7]. The general setting which we consider is of minimal supergravity in four dimensions on a compact spin manifold without boundary endowed with an Euc...

Abstract In this brief, the spontaneous symmetry breaking (SSB) of φ 4 theory in phase space, is studied. This space results from appropriate system Poincaré maps, produced both Minkowski and Euclidean ...