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In this note we discuss the collection of statements known as Arnold conjecture for Hamiltonian diffeomorphisms of closed symplectic manifolds. We provide an overview of the homological, stable and strong versions of Arnold conjecture for non-degenerate Hamiltonian systems, a few versions of Arnold conjecture for possibly degenerate Hamiltonian systems, the degenerate version of Arnold conjecture for Hamiltonian homeomorphisms and Sandon’s version of Arnold conjecture for contactomorphisms.
In this paper, history of reserches for minimal immersions from constant Gaussian curvature 2-manifolds into space forms is explained with special emphasis of works of O. Borůvka. Then recent results for the corresponding probrem to classify minimal immersions of such surfaces in complex space forms are discussed.
In this paper, we examine the properties of hypersurfaces of weakly and pseudo concircular symmetric manifolds and we give an example for these manifolds.
We introduce a type of non-flat Riemannian manifolds called weakly cyclic Ricci symmetric manifolds and study their geometric properties. The existence of such manifolds is shown by several non-trivial examples.
The object of the present paper is to study weakly symmetric manifolds admitting a type of semi-symmetric non-metric connection.
The object of the present paper is to study weakly -symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly -symmetric manifold both the decompositions are weakly Ricci symmetric.
The object of the present paper is to study weakly -symmetric and weakly -Ricci symmetric Kenmotsu manifolds. It is shown that weakly -symmetric and weakly -Ricci symmetric Kenmotsu manifolds are -Einstein.
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