We show that certain classes of contact 3–manifolds do not admit non-separating contact type embeddings into any closed symplectic 4–manifolds, e.g. this is the case for all contact manifolds that are (partially) planar or have Giroux torsion. The latter implies that manifolds with Giroux torsion do not admit contact type embeddings into any closed symplectic 4–manifolds. Similarly, there are s...

Ambrose, Palais and Singer [6] introduced the concept of second order structures on finite dimensional manifolds. Kumar and Viswanath [23] extended these results to the category of Banach manifolds. In the present paper all of these results are generalized to a large class of Fréchet manifolds. It is proved that the existence of Christoffel and Hessian structures, connections, sprays and dissec...

This paper presents an overview of various matrix manifolds that are commonly used in computer vision applications. It covers the following manifoldsLie groups, Stiefel manifolds, Grassmann manifolds and Riemannian manifolds. A manifold of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has ...

We give explicit construction of vertex-transitive tight triangulations of d-manifolds for d ≥ 2. More explicitly, for each d ≥ 2, we construct two (d + 5d + 5)-vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated d-manifolds wit...

We show that the dynamics of automorphisms on all projective complex manifolds X (of dimension 3, or of any dimension but assuming the Good Minimal Model Program or Mori’s Program) are canonically built up from the dynamics on just three types of projective complex manifolds: complex tori, weak Calabi-Yau manifolds and rationally connected manifolds. As a by-product, we confirm the conjecture o...

A review of the geometry of 3-dimensional contact metric manifolds shows that generalized Sasakian manifolds and η-Einstein manifolds are deeply interrelated. For example, it is known that a 3-dimensional Sasakian manifold is η-Einstein. In this paper, we discuss the relationships between several special classes of 3-dimensional contact metric manifolds which are generalizations of 3-dimensiona...

1 Geometry of Manifolds 3 1.1 Definition of smooth manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Tangent space to a manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Vector fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Smooth functions on manifolds, partitions of unity. . . . . . . . . . . . . . . 22 1.5 Immers...

We propose a class of projective manifolds with degenerate secant varieties, which class is wider than that of Scorza varieties , and study some properties of this class of manifolds. For example, we show that there is a strong restriction on dimensions of manifolds in this class. We also give classiications of such manifolds of low dimensions.