A New Intrinsic Curvature Invariant for Centroaane Hypersurfaces

Minimal hypersurfaces in H × R, total curvature and index

In this paper, we consider minimal hypersurfaces in the product space Hn × R. We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal hypersurfaces with finite total curvature. This assumption implies that the corresponding curvature goes to zero uniformly at infinity. We show that surfaces with finite total int...

Complete Manifolds with Nonnegative Curvature Operator

In this short note, as a simple application of the strong result proved recently by Böhm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of Böhm and Wilking, we show that any complete Riemannian manifold (with dimension ≥ 3) whose curvature operator is bounded and satisfies the pinching condition ...

Conformally invariant bending energy for hypersurfaces

The most general conformally invariant bending energy of a closed four-dimensional surface, polynomial in the extrinsic curvature and its derivatives, is constructed. This invariance manifests itself as a set of constraints on the corresponding stress tensor. If the topology is fixed, there are three independent polynomial invariants: two of these are the straighforward quartic analogues of the...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Cosmological perturbation theory and conserved quantities in the large-scale limit

The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on hypersurfaces of constant expansion, constant curvature or constant energy density. The existence of conserved perturbation quantities on scales larger than th...