On the non-existence of certain ovaloids
On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture
Let M̅ be a compact Riemannian manifold with sectional curvature satisfying (resp. ), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in M̅. This extends Shen and Xu’s result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.
On the nullity index of isometric immersions of Kähler manifolds
On the operator of exterior derivation on the Riemannian manifolds with cylindrical ends.
On the Polynomial Cohomology of Affine Manifolds.
On the problem whether the image of a given differentiable map into Riemannian manifold is contained in a submanifold with parallel second fundamental form.
On the projections of Laplacians under Riemannian submersions.
On the Regularity of Minimal Surfaces with Free Boundaries in Riemannian Manifolds.
On the Resolution of Degenerate Closed Geodescis.
On the Ricci operator of locally homogeneous Lorentzian 3-manifolds
We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.
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