It is shown that there are plenty of hyperbolic-elliptic invariant tori, thus quasiperi-odic solutions for a class of nonlinear wave equations.

We consider the problem of varying conformally the metric of a four dimensional manifold in order to obtain constant Q-curvature. The problem is variational, and solutions are in general found as critical points of saddle type. We show how the problem leads naturally to consider the set of formal barycenters of the manifold.

For a d-dimensional real hyperbolic manifold with cusps, we obtain more refined error terms in the prime geodesic theorem (PGT) using the Ruelle zeta function instead of the Selberg zeta function. To do this, we prove that the Ruelle zeta function over this type manifold is a meromorphic function of order d over C.

We study the manifold of all metrics with the fixed volume form on a compact Riemannian manifold of dimension ≥ 3. We compute the characteristic function for the L (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics, and give applications to the diameter and eigenvalue functionals.

The idea of reconstructing of geometry of riemannian manifold M from the Brownian motion on M has been productively explored for a long time (see, for instance, expository article of Pinsky [7] and references therein). In [7] different asymptotics of Brownian motion (mean exit time, distribution of exit time from small ball,...) has been produced and it was shown that it is possible to retrieve...

New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can get twisted, warped or direct decompositions. Some applications to Lorentzian manifold are shown and also S ×L type decomposition is treated.

Let (M4, g, ω) be a compact, almost-Kähler Einstein manifold of negative star-scalar curvature. Then (M,ω) is a minimal symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected sum N#CP2.

The tangent bundle as a 4n-manifold is equipped with an almost hypercomplex pseudo-Hermitian structure and it is characterized with respect to the relevant classifications. A number of 8-dimensional examples of the considered type of manifold are received from the known explicit examples in that manner.

If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the manifold and its boundary. So essentially, Euler characteristic is the unique invariant of this type.

In this paper, the geometry of F -invariant CR-submanifolds of a Kaehlerian product manifold is studied. Fundamental properties of this type submanifolds are investigated such as CR-product, D⊥-totally geodesic and mixed geodesic submanifold. Finally, we have researched totally-umbilical F -invariant proper CR-submanifolds and CR-products in a Kaehlerian product manifold M = M1(c1)×M2(c2) M.S.C...