In this paper we make the first steps towards developing a theory of intersections of coisotropic submanifolds, similar to that for Lagrangian submanifolds. For coisotropic submanifolds satisfying a certain stability requirement we establish persistence of coisotropic intersections under Hamiltonian diffeomorphisms, akin to the Lagrangian intersection property. To be more specific, we prove tha...

Special Lagrangian submanifolds of complex Euclidean space C have been studied widely over the last few years. These submanifolds are volume minimizing and, in particular, they are minimal submanifolds. When n = 2, special Lagrangian surfaces of C are exactly complex surfaces with respect to another orthogonal complex structure on R ≡ C. A very important problem here, and even a good starting p...

The purpose of this paper is to study the second fundamental form of some submanifolds M in Euclidean spaces E" which have flat normal connection. As such, Theorem gives precise expressions for the (essentially 2) Weingarten maps of all 4-dimensional Emstem submanifolds in E6, which are specialized in Corollary 2 to the Rcciflat submanifolds. The main part ofthis paper deals with fiat submanifo...

This paper aims to present work on contact pseudo-slant submanifolds of Para-Sasakian manifold. The study includes the definitions and some results type 1, 2, 3 submanifolds.

We obtain new restrictions on Maslov classes of monotone Lagrangian submanifolds $\mathbb{C}^n$. also construct families examples submanifolds, which show that the are sharp in certain cases.

We discuss existence and classification of totally umbilic surfaces in the model geometries of Thurston and the Berger spheres. We classify such surfaces in H × R, S × R and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.

The second variation operator of minimal submanifolds of Riemannian manifolds (the Jacobi operator) carries information about stability properties of the submanifold when it is thought of as a critical point for the area functional. When the ambient Riemannian manifold is a sphere S, Simons [S] characterized the totally geodesic submanifolds as the minimal submanifolds of S either with the lowe...

This paper presents diierent examples of enumerative geometry in robotics and vision. The aim is to obtain intersection formulas giving the number of solutions (on C) of some classes of problems which appear in such applied elds. The rst family of examples involves curves and surfaces dealing with distances. In such problems, the varieties have a common part at innnity, called the umbilic, that...

By a theorem of Mclean, the deformation space of an associative submanifold Y of an integrable G2-manifold (M,φ) can be identified with the kernel of a Dirac operator D/ : Ω(ν) → Ω(ν) on the normal bundle ν of Y . Here, we generalize this to the non-integrable case, and also show that the deformation space becomes smooth after perturbing it by natural parameters, which corresponds to moving Y t...

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. Recently, B.-Y. Chen studied Lagrangian submanifolds in complex space forms which are ideal. He proved that such submanifolds are minimal. He also classified ideal Lagrangian submani...