In recent years, substantial progress in shape analysis has been achieved through methods that use the spectra and eigenfunctions of discrete Laplace operators. In this work, we study spectra and eigenfunctions of discrete differential operators that can serve as an alternative to the discrete Laplacians for applications in shape analysis. We construct such operators as the Hessians of surface ...

Ž . ABSTRACT: We introduce TheRate THEoretical RATEs , a complete Ž . application program with a graphical user interface GUI for calculating rate constants from first principles. It is based on canonical variational transition-state Ž . theory CVT augmented by multidimensional semiclassical zero and small Ž . curvature tunneling approximations. Conventional transition-state theory TST with one...

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.

In this article, we derived an equality for CR-warped product in a complex space form which forms the relationship between gradient and Laplacian of warping function second fundamental form. We necessary conditions submanifolds Ka¨hler manifold to be Einstein impact Ricci soliton. Some classification by using Euler–Lagrange equation, Dirichlet energy Hamiltonian is given. also derive some chara...

In this paper, we prove that, for compact warped product submanifolds Mn in an Euclidean space En+k, there are no stable p-currents, homology groups vanishing, and M3 is homotopic to the sphere S3 under various extrinsic restrictions, involving eigenvalue of function, integral Ricci curvature, Hessian tensor. The results paper can be considered extension Xin’s work framework a submanifold, when...

The investigation of manifolds with non-negative sectional curvature is one of the classical fields of study in global Riemannian geometry. While there are few known obstruction for a closed manifold to admit metrics of non-negative sectional curvature, there are relatively few known examples and general construction methods of such manifolds (see [Z] for a detailed survey). In this context, it...

Let X : (S, g) → R be a C isometric embedding of a C 4 metric g of non-negative sectional curvature on S into the Euclidean space R. We prove a priori bounds for the trace of the second fundamental form H , in terms of the scalar curvature R of g, and the diameter d of the space (S, g). These estimates give a bound on the extrinsic geometry in terms of intrinsic quantities. They generalize esti...

One of the basic problems of Riemannian geometry is the classification of manifolds of positive sectional curvature. The known examples include the spherical space forms which carry constant curvature metrics and the rank 1 symmetric spaces whose canonical metrics have sectional curvatures at each point varying between 1 and 4. In 1951 H.E. Rauch [18] introduced the notion of curvature pinching...

In this paper, we prove that a complete noncompact non-flat conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton. 1. The result A complete Riemannian metric gij on a smooth manifold M n is called a gradient steady Ricci soliton if there exists a smooth function F on M such that the Ricci tensor Rij of the metric gij is given by the Hessian of F : Rij = ∇i∇jF. (1....