In this article, we first consider the L2 Morse–Novikov cohomology on a complete Riemannian manifold M equipped with parallel 1-form which includes Vaisman manifold. Based vanishing theorem of cohomology, prove that L2-harmonic forms are identically zero.

The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.

We give a method for performing the center manifold reduction that eliminates the need to transform the original equations of motion into eigencoordinates To achieve this we write the center manifold as an embedding rather than as a graph over the center subspace Introduction The center manifold reduction is a technique for eliminating non essential degrees of freedom in bifurcation problems Th...

Strata in manifold stratified spaces are shown to have neighborhoods that are teardrops of manifold stratified approximate fibrations (under dimension and compactness assumptions). This is the best possible version of the tubular neighborhood theorem for strata in the topological setting. Applications are given to replacement of singularities, to the structure of neighborhoods of points in mani...

We prove entropy rigidity for finite volume strictly convex projective manifolds in dimensions $$\ge 3$$ , generalizing the work of [1] to setting. The theorem uses techniques Besson, Courtois, and Gallot’s theorem. It implies uniform lower bounds on any manifold .

In this paper, we have defined recurrence and symmetry of different kinds in Hsu-structure manifold. Some theorem establishing relationship between recurrent H- HSU-Structure manifold involving equivalent conditions with respect to projective, conformal, conharmonic concircular curvature tensors has been discussed parameter also studied.

The main purpose of the following article is to give a proof of Y. Kawa-mata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an L 2 m –extension theorem of Ohsawa-Takegoshi type (which is also a new result) and a more complete version of our former results. §0 Introduction Let X be a projective manifold and let Θ be a ...