Nonlinear connections on dual Lie algebroids.
Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations.
Non-minimal Yang-Mills fields and dynamics.
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres
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.
Nonnegatively Curved Totally Real Submanifolds.
Nonnegativity for the Curvature Operator and Isotropy for Isometric Immersions.
Non-parametric convex hypersurfaces with a curvature restriction
Nonpositively curved metrics on 2-polyhedra.
Non-rational minimal spheres and minimizing cones.
Non-Realizable CR Structures.
Nonresonance conditions for arrangements
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
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...
Non-standard Einstein extensions of five dimensional nilpotent metric Lie algebras.
Nonstandard uniformized conformal structures on hyperbolic manifolds.
Nonsymmetric weakly complete G-spaces
Nontaut foliations and isoperimetric constants
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
Non-Trapping sets and Huygens Principle
We consider the evolution of a set 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
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.
Nonuniqueness for the heat flow of harmonic maps