The fundamental theorems of curves and hypersurfaces in centro-affine geometry.
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 gap theorems for some extremal submanifolds in a unit sphere
Let be an -dimensional submanifold in the unit sphere , we call a -extremal submanifold if it is a critical point of the functional . In this paper, we can study gap phenomenon for these submanifolds.
The Gauss and Gauss-Codazzi-Ricci equations for rheonomous anholonomic manifold
The Gauss Map for Surfaces in 4-Space.
The Gauss map of a spacelike constant mean curvature hypersurface of Minkowski space.
The Gauss map of Hessian manifolds in spaces of constant Hessian sectional curvature via Kozsul forms.
The Gauss-Bonnet theorem for Cayley-Klein geometries of dimension two.
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 generalized -algebra structure on BGG sequences and generalized associative operad
The generalized Holditch theorem for the homothetic motions on the planar kinematics
W. Blaschke and H. R. Müller [4, p. 142] have given the following theorem as a generalization of the classic Holditch Theorem: Let be a 1-parameter closed planar Euclidean motion with the rotation number and the period . Under the motion , let two points , trace the curves and let be their orbit areas, respectively. If is the orbit area of the orbit curve of the point which is collinear with points and then In this paper, under the 1-parameter closed planar homothetic motion...
The generalized Lichnerowicz formula and analysis of Dirac operators.
The generalized regular functions over conformal quaternionic manifold
The geodesic curvature and geodesic torsion of the intersection curve of two surfaces.
The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds
The geography of simply-connected symplectic manifolds
By using the Seiberg-Witten invariant we show that the region under the Noether line in the lattice domain is covered by minimal, simply connected, symplectic 4-manifolds.
The geometric quantization of the moduli space of Riemann surfaces with even spin structure.
The geometric structure of the inverse gamma distribution.
The geometric structure of the Pareto distribution.