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On some spaces which are covered by a product space

Izu Vaisman (1977)

Annales de l'institut Fourier

In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the...

On the Cech bicomplex associated with foliated structures

Haruo Kitahara, Shinsuke Yorozu (1978)

Annales de l'institut Fourier

For a codimension q foliation on a manifold, η × ( d η ) q defines the Godbillon-Vey class. We show that η itself defines a certain cohomology class, via the Cech bicomplex.

On the first secondary invariant of Molino's central sheaf

Jesús A. Álvarez López (1996)

Annales Polonici Mathematici

For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.

On the group of real analytic diffeomorphisms

Takashi Tsuboi (2009)

Annales scientifiques de l'École Normale Supérieure

The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the n -dimensional torus, its identity component is a simple group. For U ( 1 ) fibered manifolds, for manifolds admitting special semi-free U ( 1 ) actions and for 2- or 3-dimensional manifolds with nontrivial U ( 1 ) actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.

On the structure of a Morse form foliation

I. Gelbukh (2009)

Czechoslovak Mathematical Journal

The foliation of a Morse form ω on a closed manifold M is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of M and ω . Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of rk ω and Sing ω . The set of the ranks of all forms defining a given foliation without minimal...

Currently displaying 281 – 300 of 439