On the geometric meaning of the classical equation of Gauss.
On the geometry of tangent bundles with a class of metrics
We introduce a class of metrics on the tangent bundle of a Riemannian manifold and find the Levi-Civita connections of these metrics. Then by using the Levi-Civita connection, we study the conformal vector fields on the tangent bundle of the Riemannian manifold. Finally, we obtain some relations between the flatness (resp. local symmetry) properties of the tangent bundle and the flatness (resp. local symmetry) on the base manifold.
On the harmonic and Killing tensor field on a compact Riemannian manifold.
On the Heat Equation and the Index Theorem.
On the Index of Callias-type Operators.
On the Initial-Boundary Value Problem for Harmonic Maps from the 2-Dimensional Minkowski Space.
On the intrinsic geometry of a unit vector field
We study the geometrical properties of a unit vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature , we give a description of the totally geodesic unit vector fields for and and prove a non-existence result for . We also found a family of vector fields on the hyperbolic 2-plane of curvature which generate foliations on with leaves of constant intrinsic...
On the irreducibility and inequivalence of unitary representations of gauge groups
On the Killing tensor fields on a compact Riemannian manifold.
On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
The Martin compactification of a bounded Lipschitz domain is shown to be for a large class of uniformly elliptic second order partial differential operators on .Let be an open Riemannian manifold and let be open relatively compact, connected, with Lipschitz boundary. Then is the Martin compactification of associated with the restriction to of the Laplace-Beltrami operator on . Consequently an open Riemannian manifold has at most one compactification which is a compact Riemannian...
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.