A contact stationary Legendrian submanifold of S is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contact stationary Legendrian submanifold (actually minimal and Legendrian) is the real, equatorial n-sphere S0. This paper develops a method for constructing contact stationary (but not minimal) Legendrian submanifolds of S by gluing together configur...

We solve the generalized Milnor–Hirzebruch problem on the relations between Chern numbers of an arbitrary stably almost complex manifold and Chern numbers of its virtual Chern submanifolds. As a corollary we derive new divisibility conditions for Chern classes of an arbitrary complex vector bundle over a stably almost complex manifold. Introduction The generalized Milnor–Hirzebruch problem was ...

The exceptional Dehn filling conjecture of the second author concerning the relationship between exceptional slopes α, β on the boundary of a hyperbolic knot manifold M has been verified in all cases other than small Seifert filling slopes. In this paper we verify it when α is a small Seifert filling slope and β is a toroidal filling slope in the generic case where M admits no punctured-torus f...

In this paper, we propose an approach for automatic generation of novel intrusion signatures. This approach can be used in the signature-based Network Intrusion Detection Systems (NIDSs) and for the automation of the process of intrusion detection in these systems. In the proposed approach, first, by using several one-class classifiers, the profile of the normal network traffic is established. ...

The notion the spread of a matrix was first introduced fifty years ago in algebra. In this article, we define the spread of the shape operator by applying the same idea to submanifolds of Riemannian manifolds. We prove that the spread of shape operator is a conformal invariant for any submanifold in a Riemannian manifold. Then, we prove that, for a compact submanifold of a Riemannian manifold, ...

We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its “boundary depth,” and establish basic results about how the boundary depths of different Hamiltonians are related. As applications, we prove that certain Hamiltonian symplectomorphisms supported in displaceable subsets have infinitely many nontrivial geometrically distinct periodic ...

Let x : M → Sn+p be an n-dimensional submanifold in an (n + p)dimensional unit sphere Sn+p, x : M → Sn+p is called a Willmore submanifold if it is an extremal submanifold to the following Willmore functional: ∫ M (S − nH) 2 dv, where S = ∑ α,i,j (hij) 2 is the square of the length of the second fundamental form, H is the mean curvature of M . In [13], author proved an integral inequality of Sim...

Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if ...

A contact-stationary Legendrian submanifold of S2n+1 is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contactstationary Legendrian submanifold (actually minimal Legendrian) is the real, equatorial n-sphere S0. This paper develops a method for constructing contact-stationary (but not minimal) Legendrian submanifolds of S2n+1 by gluing together confi...

This is the first article of the two papers in which we investigate the holomorphic and formal flattening problem for a codimension two real submanifold in C with n ≥ 3 near a non-degenerate CR singular point. The problem is motivated from the study of the complex Plateau problem that seeks for the Levi-flat hypersurface bounded by a given real submanifold and is motivated by the classical comp...