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We study contact structures on nonnegatively graded manifolds equipped with homological contact vector fields. In the degree 1 case, we show that there is a one-to-one correspondence between such structures (with fixed contact for...
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We study contact structures on nonnegatively graded manifolds equipped with homological contact vector fields. In the degree 1 case, we show that there is a one-to-one correspondence between such structures (with fixed contact form) and Jacobi manifolds. This correspondence allows us to reinterpret the Poissonization procedure, taking Jacobi manifolds to Poisson manifolds, as a supergeometric version of symplectization.
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For asymptotically hyperbolic manifolds of dimension n with scalar curvature at least equal to -n(n - 1) the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to...
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For asymptotically hyperbolic manifolds of dimension n with scalar curvature at least equal to -n(n - 1) the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero.
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In this article, we give an alternative proof for the convergence of the K?hler-Ricci flow on a Fano manifold (M, J). The proof differs from the one in our previous paper [J. Amer. Math. Sci. 17 (2006), 675-699]. Moreover, we gene...
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In this article, we give an alternative proof for the convergence of the K?hler-Ricci flow on a Fano manifold (M, J). The proof differs from the one in our previous paper [J. Amer. Math. Sci. 17 (2006), 675-699]. Moreover, we generalize the main theorem given there to the case that (M, J) may not admit any K?hler-Einstein metrics.
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In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H5/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 52 of the group Γ 5 of positi...
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In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H5/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 52 of the group Γ 5 of positive units of the Lorentzian quadratic form x_1^{2}+\\cdots +x_{5}^{2}-x_6^{2}. We also show that Γ 52 is a reflection group with respect to a 5-dimensional right-angled convex polytope in H5. As an application, we construct a hyperbolic 5-manifold of smallest known volume 7ζ (3)/4.
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Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics includin...
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Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.
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Virtual 3-manifolds were introduced by Matveev in 2009 as natural generalizations of classical 3-manifolds. In this paper, we introduce a notion of complexity for a virtual 3-manifold. We investigate the values of the complexity f...
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Virtual 3-manifolds were introduced by Matveev in 2009 as natural generalizations of classical 3-manifolds. In this paper, we introduce a notion of complexity for a virtual 3-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two 2-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic 3-manifolds with totally geodesic boundary.
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The aim of this paper is to construct a 1-parameter family of Sasakian manifold starting from a single Sasakian manifold. Concrete examples are given.
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The purpose of this paper is to study a new class of contact manifolds. Such manifolds are called almost f-cosymplectic manifolds. Several tensor conditions are studied for such type of manifolds. We conclude our results with two ...
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The purpose of this paper is to study a new class of contact manifolds. Such manifolds are called almost f-cosymplectic manifolds. Several tensor conditions are studied for such type of manifolds. We conclude our results with two examples of almost f-cosymplectic manifolds.
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The notion of Ricci Riemannian manifold is introduced and some properties of such a manifoldare obtained. The existence of such a 3-dimensional manifold has been shown.
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Cartesian product of two manifolds has been defined and studied by Petrov among others. In this paper, we have considered cartesian product space of r - manifolds where r is some finite integer. Some properties of such a product m...
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Cartesian product of two manifolds has been defined and studied by Petrov among others. In this paper, we have considered cartesian product space of r - manifolds where r is some finite integer. Some properties of such a product manifold have been defined and studied. The curvature of the product manifold is also studied and it has been shown that the product manifold is an Einstein space if the manifolds M_1, M_2, M_r are Einstein spaces.
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