We provide a classification theorem for compact stable minimal immersions (CSMI) of codimension 1 or dimension (codimension and 2 2) in the product complex (quaternionic) projective space with any other Riemannian manifold. characterize as only CSMI two spaces. As an application, we rank one symmetric space.

The center manifold theorem is a model reduction technique for determining the local asymptotic stability of an equilibrium of a dynamical system when its linear part is not hyperbolic. The overall system is asymptotically stable if and only if the center manifold dynamics is asymptotically stable. This allows for a substantial reduction in the dimension of the system whose asymptotic stability...

We prove a direct analogue of the classical Duflo formula in the case of L∞algebras. We conjecture an analogous formula in the case of an arbitrary Q-manifold. When G is a compact connected Lie group, the Duflo theorem for the Q-manifold (ΠTG, dDR) is exactly the Duflo theorem for the Lie algebra g = LieG. The corresponding theorem for the Q-manifold (ΠTM,dDR), where M is an arbitrary smooth ma...

We use a notion (introduced in Topology 41 (2002), 1119–1212), which is stronger than the concept of filtration pair, to prove a stable/unstable manifold general theorem for local homeomorphisms of the plane in a neighborhood of an isolated fixed point.

The notion of flat $\lambda$-connections as the interpolation usual connections and Higgs fields was suggested by Deligne further studied Simpson. Mochizuki established Kobayashi--Hitchin-type theorem for $\lambda$-flat bundles ($\lambda\neq 0$), which is called correspondence. In this paper, on one hand, we generalize Mochizuki's result to case when base being a compact balanced manifold, more...

the main objective of this paper is to find the necessary and sufficient condition of a given finslermetric to be einstein in order to classify the einstein finsler metrics on a compact manifold. the consideredeinstein finsler metric in the study describes all different kinds of einstein metrics which are pointwiseprojective to the given one. this study has resulted in the following theorem tha...

We use veering triangulations to study homology classes on the boundary of cone over a fibered face compact hyperbolic three-manifold. This allows us give handson proof an extension Mosher’s transverse surface theorem setting manifolds with boundary. also show that is dual generated by canonical finite collection curves called minimal stable loops living in associated triangulation.

In [3] and [7] are described the Krichever map from the set of torsion free sheaves on curves with some additional datas to an infinite-dimensional Grassmanian manifold. In this note we investigate the images of (semi)stable rank 2 torsion free sheaves on curves via the Krichever map and verify some analog of G.I.T. Hilbert-Mumford numerical criterion (theorem 2) with respect to actions of some...

Singularly perturbed relay systems (SPRS) in which the reduced systems have the stable periodic motions with internal sliding modes are studied. The slow motion integral manifold of such systems consists of the parts which correspond to the di erent values of relay control and the solutions may contain the jumps from one part of the slow manifold to another. For such systems a theorem about exi...