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A new class of almost complex structures on tangent bundle of a Riemannian manifold

Amir Baghban, Esmaeil Abedi (2018)

Communications in Mathematics

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced ( 0 , 2 ) -tensor on the tangent bundle using these structures and Liouville 1 -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

A special type of triangulations in numerical nonlinear analysis.

J. M. Soriano (1990)

Collectanea Mathematica

To calculate the zeros of a map f : Rn → Rn we consider the class of triangulations of Rn so that a certain point belongs to a simplex of fixed diameter and dimension. In this paper two types of this new class of triangulations are constructed and shown to be useful to calculate zeros of piecewise linear approximations of f.

Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.

Jan Kurek, Wlodzimierz M. Mikulski (2006)

Extracta Mathematicae

We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr0 (R;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TrM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σrk=0 αkω(k) for all real numbers αk with αr ≠ 0, where ω(k) is the (k)-lift (in the sense of A. Morimoto) of ω to TrM.

Cohomologie de dolbeault le long des feuilles de certains feuilletages complexes

Aziz El Kacimi Alaoui, Jihène Slimène (2010)

Annales de l’institut Fourier

La cohomologie de Dolbeault feuilletée mesure l’obstruction à résoudre le problème de Cauchy-Riemann le long des feuilles d’un feuilletage complexe. En utilisant des méthodes de cohomologie des groupes, nous calculons cette cohomologie pour deux classes de feuilletages : i) le feuilletage complexe affine de Reeb de dimension (complexe) 2 sur la variété de Hopf de dimension 5 ; ii) les feuilletages complexes sur le tore hyperbolique (fibration en tores de dimension n au-dessus d’un cercle et de monodromie...

Conformal curvature for the normal bundle of a conformal foliation

Angel Montesinos (1982)

Annales de l'institut Fourier

It is proved that the normal bundle ℋ of a distribution 𝒱 on a riemannian manifold admits a conformal curvature C if and only if 𝒱 is a conformal foliation. Then ℋ is conformally flat if and only if C vanishes. Also, the Pontrjagin classes of ℋ can be expressed in terms of C .

Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions

Dmitri V. Alekseevsky, Ricardo Alonso-Blanco, Gianni Manno, Fabrizio Pugliese (2012)

Annales de l’institut Fourier

We study the geometry of multidimensional scalar 2 n d order PDEs (i.e. PDEs with n independent variables), viewed as hypersurfaces ℰ in the Lagrangian Grassmann bundle M ( 1 ) over a ( 2 n + 1 ) -dimensional contact manifold ( M , 𝒞 ) . We develop the theory of characteristics of ℰ in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of ℰ . After specializing such results to general Monge-Ampère equations (MAEs), we focus our attention to MAEs of...

Contact hamiltonians distinguishing locally certain Goursat systems

Piotr Mormul (2000)

Banach Center Publications

For the first time in dimension 9, the Goursat distributions are not locally smoothly classified by their small growth vector at a point. As shown in [M1], in dimension 9 of the underlying manifold 93 different local behaviours are possible and four irregular pairs of them have coinciding small growth vectors. In the present paper we distinguish geometrically objects in three of those pairs. Smooth functions in three variables - contact hamiltonians in the terminology of Arnold, [A] - help to do...

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