We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using this we produce a method of constructing simply connected K-contact non-Sasakia...

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 establish a compact analogue of the P=W conjecture. For projective irreducible holomorphic symplectic variety with Lagrangian fibration, we show that perverse numbers associated fibration match perfectly Hodge total space. This builds new connection between topology fibrations and theory hyper-Kähler manifolds. present two applications our result: one on cohomology base fibers other refined ...

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...

In this report we make a thorough study of the Chern–Simons field theory for compact oriented 3–manifolds associated to a compact simply connected simple Lie group G mainly following [F]. The action of the classical Wess–Zumino–Witten theory in 1 + 1 dimensions appears in Chern–Simons theory in the definition of the Hermitian line corresponding to the boundary of a 3–manifold. A part of the rep...

In this article, we study the higher-order regularity of Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates cylinders, proved that when generic fibers Iitaka fibration are biholomorphic to each other, converges in C loc ? -topology away from singular a negative Kähler-Einstein metric base manifold. particular...

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...

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These...

We consider compact Kähler manifolds acted on by a connected compact Lie group K of isometries in a Hamiltonian fashion. We prove that the squared moment map ||μ|| is constant if and only if the manifold is biholomorphically and K-equivariantly isometric to a product of a flag manifold and a compact Kähler manifold which is acted on trivially by K. The authors do not know whether the compactnes...

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These...