An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.
We discuss conditions under which a symplectic 4-manifold has a compatible Kähler structure. The theory of -holomorphic embedded spheres is extended to the immersed case. As a consequence, it is shown that a symplectic 4-manifold which has two different minimal reductions must be the blow-up of a rational or ruled surface.
A submanifold of the Euclidean space is said to be infinitesimally rigid if any smooth variation which is isometric to first order is trivial. The main purpose of this paper is to show that local or global conditions which are well known to imply isometric rigidity also imply infinitesimal rigidity.
In this paper, we study closed -maximal spacelike hypersurfaces in anti-de Sitter space with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
In this paper we prove that each -natural metric on a linear frame bundle over a Riemannian manifold is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define -natural metrics on the orthonormal frame bundle and we prove the same invariance result as above for . Hence we see that, over a space of constant sectional curvature, the bundle with an arbitrary -natural metric is locally homogeneous.