We deal with a CR-submanifold M of a para-Kählerian manifold M, which carries a J-skew-symmetric vector field X. It is shown that X defines a global Hamiltonian of the symplectic form Ω on M and JX is a relative infinitesimal automorphism of Ω. Other geometric properties are given. 1. Introduction. CR-submanifolds M of some pseudo-Riemannian manifolds M have been first investigated by Rosca [10...

Wilson loops in N = 4 supersymmetric Yang-Mills theory correspond at strong coupling to extremal surfaces in AdS5. We study a class of extremal surfaces known as special Legendrian submanifolds. The ”hemisphere” corresponding to the circular Wilson loop is an example of a special Legendrian submanifold, and we give another example. We formulate the necessary conditions for the contour on the bo...

We study the task to infer and to track the viewpoint onto a 3D rigid object by observing its image contours in a sequence of images. To this end, we consider the manifold of invariant planar contours and learn the low-dimensional submanifold corresponding to the object contours by observing the object off-line from a number of different viewpoints. This submanifold of object contours can be pa...

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9-dimensional submanifold of the 12-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. This freedom...

Let M̄ be a complex space form of constant holomorphic sectional curvature c and let M be an n-dimensional CR-submanifold of (n− 1) CR-dimension in M̄. ThenM has an almost contact metric structure (F,U ,u,g) (see Section 2) induced from the canonical complex structure of M̄. Hence on an n-dimensional CR-submanifold of (n− 1) CRdimension, we can consider two structures, namely, almost contact struc...

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements and their time derivatives. We demonstrate that there exists a vast freedom in choosing this submanifold. Th...