In this paper we obtain a classification of hypersurfaces in the Euclidean sphere having two principal curvatures; for some of the results we impose that the sectional curvature (Ricci curvature, resp.) is non-negative Ricci.

We show that for any non-trivial representation (V, π) of u(2) with the center acting as multiples of the identity, the semidirect product u(2) ⋉ πV admits a metric with negative Ricci curvature that can be explicitly ...

This paper studies the metric structure of manifolds of semi-negative curvature. Explicit estimates on the geodesic distance and sectional curvature are obtained in the setting of homogeneous spaces G/K of Banach–Lie groups, ...

Recently, there has been renewed interest in the coupling between geometry and topological defects in crystalline and striped systems. Standard lore dictates that positive disclinations are associated with positive Gaussian ...

We construct many examples of Lie groups admitting a left-invariant metric of negative Ricci curvature. We study Lie algebras which are semidirect products l= (a⊕ u) ⋉ n and we obtain examples where u is any semisimple ...

Until a couple of years ago, the only known examples of Lie groups admitting left-invariant metrics with negative Ricci curvature were either solvable or semisimple.We use a general construction from a previous article of ...

We propose a modified form of the spontaneous birth of the universe by quantum tunneling. It proceeds through topology change and inflation, to eventually become a universe with closed spatial sections of negative spatial ...

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders ...

By using the Nambu–Jona-Lasinio model, we study dynamical symmetry breaking in spaces with a constant negative curvature. We show that the physical reason for the zero value of the critical coupling constant (Formula ...