On the scalar curvature of self-dual manifolds.
On the Scalar Curvature of Tangent sphere bundles with Arbitary Constant Radius
On the singular set of stationary harmonic maps.
On the Sobolev constant and the -spectrum of a compact riemannian manifold
On the Structure of Manifolds with positive Scalar Curvature.
On the structure of Riemannian manifolds of almost nonnegative Ricci curvature.
On the Structures of Positively Curved Manifolds with Certain Diameter.
On the topological charge conservation in the three-dimensional -model.
A field of three-component unit vectors on the dimensional spacetime is considered. Two field configurations with different values of the topological charge cannot be connected by the path of field configurations with a finite Euclidean action. Therefore there is no transition between them. The initial and final configurations are assumed to be continuous at infinity. The asymptotic behaviour of intermediate configurations may be arbitrary. The proof is based on the properties of the degree of...
On the topology of positively curved Bazaikin spaces
We explore some aspects of the topology of the family of 13-dimensional Bazaikin spaces. Using the computation of their homology rings, Pontryagin classes and linking forms, we show that there is only one Bazaikin space that is homotopy equivalent to a homogeneous space, i.e., the Berger space. Moreover, it is easily shown that there are only finitely many Bazaikin spaces in each homeomorphism type and that there are only finitely many positively curved ones for a given cohomology ring. In fact,...
On the Topology of Riemann Spaces of Quasi-constant Curvature
On the Total Absolute Curvature of Closed Curves in Manifolds of Negative Curvature.
On the volume of a unit vector field on the three-sphere.
On the Wave Equation Asymptotics of a Compact Negatively Curved Surface.
On the Wave Equation on a Compact Riemannian Manifold withour Conjugate Points.
On tori without conjugate points.
On two natural Riemannian metrics on a tube.
On Uniqueness Theoremsfor Ricci Tensor
In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold and a symmetric 2-tensor , construct a metric on whose Ricci tensor equals . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative...
On Univalent Harmonic Maps Between Surfaces.
On Variations of Metrics.
Operators on eigenmaps between spheres