We introduce the operation of forming the tensor product in the theory of analytic Frobenius manifolds. Building on the results for formal Frobenius manifolds which we extend to the additional structures of Euler fields and flat identities, we prove that the tensor product of pointed germs of Frobenius manifolds exists. Furthermore, we define the notion of a tensor product diagram of Frobenius ...

Locally conformally Kähler (LCK) manifolds with potential are those which admit a Kähler covering with a proper, automorphic, global potential. Existence of a potential can be characterized cohomologically as vanishing of a certain cohomology class, called the Bott-Chern class. Compact LCK manifolds with potential are stable at small deformations and admit holomorphic embeddings into Hopf manif...

Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both stable and unstable fast manifolds. We present two examples of bifurcation problems where these manifolds play a key role and a third example in which saddle-ty...

Stratified manifolds are encountered in the configuration manifolds of many robots. Some typical examples are the walking robots [4, 5]. The configuration manifolds of such robots are in general high dimensional with some distinctive features. The most important characteristic feature of stratified manifolds are that they are filled with discontinuities [5]. These discontinuities give rise to c...

be the Hirzebruch L-class of an oriented manifold M. Let B (or K(; 1)) denote any aspherical space with fundamental group. (A space is aspherical if it has a contractible universal cover.) In 1970 Novikov made the following conjecture. Many surveys have been written on the Novikov Conjecture. The goal here is to give an old-fashioned point of view, and emphasize connections with characteristic ...

Legendre curves play a very important and special role in geometry topology of almost contact manifolds.There are certain results known for 3-dimensional normal manifolds. The aim this paper is to study three-dimensional $C_{12}$-manifolds which non-normal manifolds classifying all biharmonic these

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex pseudoconvex domains, weakly $1$-complete manifolds covering manifolds. This paper is essentially based the asymptotic Bergman kernel functions Bochner-Kodaira-Nakano formulas.

These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms connections, frame bundles and geometry. Then we arrive main aim these notes, which is description canonical grading connection existing on sub-Riemann manifolds with constant symbol. structures are exactly what needed order determine if two isometric. three concret...

A natural notion of complexity of a PL n-dimensional manifold is the minimal number of highest-dimensional simplices in a triangulation of the manifold. Such a complexity is an integer-valued function and is finite (for each k ≥ 0 there are only finitely many manifolds whose complexity is less than or equal to k). In order to find all the n-manifolds of complexity k, one has to identify all the...

In this thesis we prove some results on symplectic structures on 4-dimensional manifolds and contact structures on 5-dimensional manifolds. We begin by discussing the relation between holomorphic and symplectic minimality for Kähler surfaces and the irreducibility of minimal simply-connected symplectic 4-manifolds under connected sum. We also prove a result on the conformal systoles of symplect...