In the recent preprint [1] S. Parrott proves the equality between the Arveson's curvature and the Fredholm index of a " pure " contraction with finite defect numbers. In the present note one derives a similar formula in the " non-pure " case. The notions of d-contraction T = (T 1 , T 2 ,. .. , T d) and its curvature was introduced by W. Arveson in a series of papers (see [2], [3], and [4]). In ...

Through of the concept of curvature energy encoded in non-harmonic signals due to the effect that characterizes the curvature as a deformation of field in the corresponding resonance space ( and an obstruction to the displacement to the corresponding shape operator) is developed and designed a sensor of quantum gravity considering the quantized version of curvature as observable of gravitationa...

In this paper, we study certain compact 4-manifolds with non-negative sectional curvature K. If s is the scalar curvature and W+ is the self-dual part of Weyl tensor, then it will be shown that there is no metric g on S2 × S2 with both (i) K > 0 and (ii) 1 6 s−W+ ≥ 0. We also investigate other aspects of 4-manifolds with non-negative sectional curvature. One of our results implies a theorem of ...

The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature ßow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive...

We will show that in the conformal class of the standard metric gSn on Sn, the scaling invariant functional g (S n) 2m n n R Sn Q2m;gd g maximizes at gSn when n is odd and m = n+1 2 or n+3 2 . For n odd and m n+5 2 , gSn is not stable and the functional has no local maximizer. Here Q2m;g is the 2mth order Q-curvature. 1. Introduction Let Ag be a di¤erential operator on a n-dimensional Riemannia...

Positiveness of scalar curvature and Ricci curvature requires vanishing the obstruction θ(M) which is computed in some KK-theory of C*-algebras index as a pairing of spin Dirac operator and Mishchenko bundle associated to the manifold. U. Pennig had proved that the obstruction θ(M) does not vanish if M is an enlargeable closed oriented smooth manifold of even dimension larger than or equals to ...

For a closed hypersurface Mn ⊂ Sn+1(1) with constant mean curvature and non-negative scalar curvature, we show that if $${\rm{tr}}\left({{{\cal A}^k}} \right)$$ are constants for k = 3, …, n − 1 the shape operator $${\cal A}$$ then M is isoparametric. The result generalizes theorem of de Almeida Brito (1990) 3 to any dimension n, strongly supporting Chern conjecture.