Collapsing and soul theorem in three-dimension
Collapsing of Riemannian manifolds and eigenvalues of La-place operator.
Collapsing Riemannian Manifolds to the Circle.
Collars in PSL.
Collective geodesic flows
We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.
Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case
This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.
Combinatorics of curvature, and the Bianchi identity.
Combinatorics of non-holonomous jets
Commensurability classes and volumes of hyperbolic 3-manifolds
Comment on curves in 2- and 3-dimensional Monkowski space.
Commutation formulas for -differentiation in a generalized Finsler space
Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms
In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results...
Commuting linear operators and algebraic decompositions
For commuting linear operators we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential...
Compact 3-manifolds with a flat Carnot-Carathéodory metric
Compact 8-manifolds with holonomy Spin (7).
Compact and small rank perturbations of conformally symplectic structures
Compact automorphic actions on an n-dimensional monoid with an (n-1) dimensional group of units.
Compact Conformally Symmetric Riemannan Spaces.
Compact constant mean curvature surfaces with low genus.
Compact cosymplectic manifolds of positive constant phi-sectional curvature.