A Construction of Non-Flat, Compact Irreducible Riemannian Manifolds Which are Isospectral But Not Isometric.
A construction of non-flat non-homogeneous symmetric parabolic geometries
We construct series of examples of non-flat non-homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.
A construction of transverse submanifolds.
A contact metric manifold satisfying a certain curvature condition
In the present paper we investigate a contact metric manifold satisfying (C) for any -geodesic , where is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any -geodesic . Also, we prove a structure theorem for a contact metric manifold with belonging to the -nullity distribution and satisfying (C) for any -geodesic .
A continuation method for motion-planning problems
We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...
A continuation method for motion-planning problems
We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...
A contribution to the Cartan's method of specialization of frames
A contribution to the connection of V. Hlavatý
A convenient setting for differential geometry and global analysis
A convenient setting for differential geometry and global analysis II
A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds
We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time existence result...
A Convergence Theorem for Immersions with <>-Bounded Second Fundamental Form
A convergent post-newtonian approximation for the constraint equations in general relativity
A convex Darboux theorem
A convexity theorem for Poisson actions of compact Lie groups
A coordinatewise formulation of geometric quantization
A correction to "A note on equichordal graphs" (Port. Math., 45(4) (1988), 363-368)
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
A counterexample to the rigidity conjecture for polyhedra
A criterion for pure unrectifiability of sets (via universal vector bundle)
Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an -measurable subset of ℝⁿ with . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle such that, for all P ∈ A, one has . One can replace “for all P ∈ A” by “for -a.e. P ∈...