Generalized cells in generalized manifolds

Generalized Cells in Generalized Manifolds

On some generalized recurrent manifolds

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...

Transversality in Generalized Manifolds

Suppose that X is a generalized n-manifold, n 5, satisfying the disjoint disks property, and M and Q are topologicalmand q-manifolds, respectively, 1-LCC embedded in X, with n m 3 and n q 3. We de ne what it means for M to be stably transverse to Q in X. In the metastable range, 3m 2(n 1) and 3(m+ q) < 4(n 1), we show that there is an arbitrarily small homotopy of M to a 1-LCC embedding that is...

Embeddings in Generalized Manifolds

We prove that a (2m n+1)-connectedmap f : Mm ! Xn from a compact PL m-manifoldM to a generalized n-manifoldX with the disjoint disks property, 3m 2n 2, is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompactM and proper maps f that are properly (2m n+ 1)-connected. The techniques developed lead to a general position result for arb...

Generalized Calabi-Yau manifolds

A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2-forms. In the special case of six dimensions we characterize them as critical points of a natural variational problem on clos...