Closed 2-forms and an embedding theorem for symplectic manifolds
نویسندگان
چکیده
منابع مشابه
On the Darboux Theorem for Weak Symplectic Manifolds
A new tool to study reducibility of a weak symplectic form to a constant one is introduced and used to prove a version of the Darboux theorem more general than previous ones. More precisely, at each point of the considered manifold a Banach space is associated to the symplectic form (dual of the phase space with respect to the symplectic form), and it is shown that the Darboux theorem holds if ...
متن کاملSymplectic Forms and Cohomology Decomposition of Almost Complex 4-manifolds
In this paper we continue to study differential forms on an almost complex 4–manifold (M,J) following [18]. We are particularly interested in the subgroups H J (M) and H − J (M) of the degree 2 real De Rham cohomology group H2(M,R). These are the sets of cohomology classes which can be represented by J-invariant, respectively, J-anti-invariant real 2−forms. The goal pursued by defining these su...
متن کاملA proof of Sobolev’s Embedding Theorem for Compact Riemannian Manifolds
Observe that H 0 (M) = L p(M). Also, Hk := H2 k is a Hilbert space under the L2-inner product. F k contains only smooth functions. In general, a sequence in F k will not converge in the H k norm to a function in F k , so we need to complete the space to have anything useful. An alternate approach would have been to start with functions in Lp rather than completing the space of smooth functions ...
متن کاملThe Space of Symplectic Structures on Closed 4-manifolds
Let X be a 2n−dimensional smooth manifold. A 2−form ω on X is said to be non-degenerate if, for each q ∈ X and for each nonzero vector v in the tangent space TqX, there is a tangent vector v ∈ TqX such that ω(u, v) 6= 0. A symplectic structure onX is a non-degenerate closed 2−form. The fundamental example of a symplectic structure is ω0 = ∑ i dxi ∧ dyi on R = {(x1, y1, ..., xn, yn)}. In fact, b...
متن کاملSome forms of the closed graph theorem
In this paper we shall establish some forms of the closed, graph theorem for locally convex spaces, using the approach of Ptak(l7). Our interest is in classifying pairs of locally convex spaces (E, F) which have the property that every closed graph linear mapping T: E -> F is continuous; if (E,F) has this property then we shall say that (E, F) is in the class *&. \is# is a particular class of l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1977
ISSN: 0022-040X
DOI: 10.4310/jdg/1214433984