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Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres

Karsten Grove, Luigi Verdiani, Burkhard Wilking, Wolfgang Ziller (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case when both are equal to two, where existence of non-negatively curved metrics is known.

Nonresonance conditions for arrangements

Daniel C. Cohen, Alexandru Dimca, Peter Orlik (2003)

Annales de l’institut Fourier

We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing theorems, and used to study Milnor fibers of line arrangements, and hypersurface arrangements.

Non-split almost complex and non-split Riemannian supermanifolds

Matthias Kalus (2019)

Archivum Mathematicum

Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. For almost complex structures, the existence of a splitting is equivalent to the existence of local coordinates in which the almost complex structure can be represented by a purely numerical matrix, i.e. containing no Grassmann variables. For Riemannian metrics, terms up to degree 2 are allowed in...

Nontaut foliations and isoperimetric constants

Konrad Blachowski (2002)

Annales Polonici Mathematici

We study nontaut codimension one foliations on closed Riemannian manifolds. We find an estimate of some constant derived from the mean curvature function of the leaves of a foliation by some isoperimetric constant of the manifold. Moreover, for foliated 2-tori and the 3-dimensional unit sphere, we find the infimum of the former constants for all nontaut codimension one foliations.

Non-Trapping sets and Huygens Principle

Dario Benedetto, Emanuele Caglioti, Roberto Libero (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the evolution of a set Λ ⊂ ℝ 2 according to the Huygens principle: i.e. the domain at time t>0, Λt, is the set of the points whose distance from Λ is lower than t. We give some general results for this evolution, with particular care given to the behavior of the perimeter of the evoluted set as a function of time. We define a class of sets (non-trapping sets) for which the perimeter is a continuous function of t, and we give an algorithm to approximate the evolution. Finally we restrict...

Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections

Julien Keller, Christina Tønnesen-Friedman (2012)

Open Mathematics

We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.

Currently displaying 81 – 100 of 116