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This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic ...
In this paper we describe the topology of 4-dimensional closed orientable Riemannian manifolds with a uniform lower bound of sectional curvature and with a uniform upper bound of diameter which collap...
A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the be...
Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on th...
We consider the billiard flow of elastically colliding hard disks on the flat 2-torus and prove that no singularity manifold can locally coincide with a manifold describing future non-hyperbolicity of...
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-form...
A rather complete investigation of anisotropic Bessel potential, Besov, and H\"older spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of t...
On a compact surface endowed with any $\Spinc$ structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a B\"{a}r-type inequality for the eige...
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
We derive sufficient conditions for the vanishing of plurigenera, $p_m(J), m>0$, on compact (l|k)-strong, $\omega^l\wedge \partial\bar\partial \omega^k=0$, Kaehler manifolds with torsion. In particula...
Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),\xi)$-semi-Riemannian manifolds are classified. Som...
We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.
$(N(k),\xi)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),\xi)$-semi-Riemannian manifolds are given. Some relations involving ${\cal T}_{a}$-curvature tensor in $(N(k),\xi)...
Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds for be para-CR. Next we examine these conditions ...
In this paper, by applying the first variation formula of $f$-bi-energy given in \cite{OND}, we study $f$-biharmonic maps between doubly warped product manifolds $M\times_{(\mu,\lambda)}N$. Under impo...

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