The first eigenvalue of spacelike submanifolds in indefinite space form
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.
The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
The First Eigenvalue of the Laplacian of an Isoparametric Minimal Hypersurface in a Unit Sphere.
The ...-form and a generalized Maslov index.
The free laplacian with attractive boundary conditions
The Free Loop Space of Globally Symmetric Spaces.
The Frobenius theorem on -dimensional quantum hyperplane.
The Frölicher-Nijenhuis bracket on some functional spaces
Two fiber bundles E₁ and E₂ over the same base space M yield the fibered set ℱ(E₁,E₂) → M, whose fibers are defined as , for each x ∈ M. This fibered set can be regarded as a smooth space in the sense of Frölicher and we construct its tangent prolongation. Then we extend the Frölicher-Nijenhuis bracket to projectable tangent valued forms on ℱ(E₁,E₂). These forms turn out to be a kind of differential operators. In particular, we consider a general connection on ℱ(E₁,E₂) and study the associated...
The fundamental group and the spectrum of the Laplacian.
The Fundamental Solution for the Kohn-Laplacian ....b on the Sphere in Cn.
The Gap Phenomena of Yang-Mills Fields over the Complete Manifold.
The gap phenomenon in the dimension study of finite type systems
Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.
The gaps in the spectrum of the Schrödinger operator
We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.
The Gaussian measure on algebraic varieties
We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety is dense in the Hilbert space , where dμ denotes the volume form of M and the Gaussian measure on M.
The general rigidity result for bundles of -covelocities and -jets
Let be an -dimensional manifold and a Weil algebra of height . We prove that any -covelocity , is determined by its values over arbitrary regular and under the first jet projection linearly independent elements of . Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result without coordinate computations, which improves and generalizes the partial result obtained...
The generalization of Cellina's Fixed Point Theorem
The generalized -algebra structure on BGG sequences and generalized associative operad
The generalized Conley index and multiple solutions of semilinear elliptic problems.
The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension
The differential-geometric and topological structure of Delsarte transmutation operators and their associated Gelfand-Levitan-Marchenko type eqautions are studied along with classical Dirac type operator and its multidimensional affine extension, related with selfdual Yang-Mills eqautions. The construction of soliton-like solutions to the related set of nonlinear dynamical system is discussed.