Abstract. We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to center manifold theory. The error is shown to contain contributions associated with the numerical accuracy of the microsolver, the numerical accuracy of the macrosolver and the distance from the center manifold caused by the combi...

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

In this paper, we present a method to interactively create multi-segment, curved handles between two star-shaped faces of an orientable 2-manifold mesh or to connect two 2-manifold meshes along such faces. The presented algorithm combines a very simple 2D morping algorithm with a Hermite interpolation to construct the handle. Based on the method, we have developed a user interface tool that all...

In this work, we present a method to interactively create multi-segment, curved handles between two star-shaped faces of an orientable 2-manifold mesh or to connect two 2-manifold meshes along such faces. The presented algorithm combines a very simple 2D morping algorithm with a Hermite interpolation to construct the handle. Based on the method, we have developed a user interface tool that allo...

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

This paper advocates a novel framework for segmenting a dataset on a Riemannian manifold M into clusters lying around lowdimensional submanifolds of M . Important examples of M , for which the proposed algorithm is computationally efficient, include the sphere, the set of positive definite matrices, and the Grassmannian. The proposed algorithm constructs a data-affinity matrix by thoroughly exp...

Object recognition is a key precursory challenge in the fields of object manipulation and robotic/AI visual reasoning in general. Recognizing object categories, particular instances of objects and viewpoints/poses of objects are three critical subproblems robots must solve in order to accurately grasp/manipulate objects and reason about their environments. Multi-view images of the same object l...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.