In the space U of cubic forms of surfaces, regarded as a G-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is evaluated in terms of the asymmetry of the metric, defined here. A connection of this ratio with that reported by Berry and Hannay (1977) in the domain of Statistical Physics, i...

The main goal of our paper is the study of several classes of submanifolds of generalized complex manifolds. Along with the generalized complex submanifolds defined by Gualtieri and Hitchin in [4], [8] (we call these “generalized Lagrangian submanifolds” in our paper), we introduce and study three other classes of submanifolds. For generalized complex manifolds that arise from complex (resp., s...

The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds, and CR-submanifolds. In this paper we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamental results in this paper will be obtained.

In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, D -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained. D

The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanif...

The main goal of our paper is the study of several classes of submanifolds of generalized complex manifolds. Along with the generalized complex submanifolds defined by Gualtieri and Hitchin in [Gua], [H3] (we call these “generalized Lagrangian submanifolds” in our paper), we introduce and study three other classes of submanifolds and their relationships. For generalized complex manifolds that a...

Let X be an asymptotically hyperbolic manifold and M its conformal infinity. This paper is devoted to deduce several existence results of the fractional Yamabe problem on M under various geometric assumptions on X and M: Firstly, we handle when the boundary M has a point at which the mean curvature is negative. Secondly, we re-encounter the case when M has zero mean curvature and is either non-...

The electromagnetic fields scattered when a plane wave is incident on an oblate spheroid in the side-on orientation may be calculated using a generalization of Mie theory, and the results may be decomposed in a Debye series expansion. A number of optical caustics are observed in the computed scattered intensity for the one internal reflection portion of the Debye series for scattering angles in...

There exist polynomial identities asociated to normal form, which yield an existence and uniqueness theorem. The space of normalized real hypersurfaces has a natural group action. Umbilic point is defined via normal form. A nondegenerate analytic real hypersurface is locally biholomorphic to a real hyperquadric if and only if every point of the real hypersurface is umbilic. 0. Introduction An a...

The aim of the present paper is to study holomorphically planar conformal vector fields(HPCV) on almost alpha-cosymplectic (k,m)-spaces. This done assuming various conditions such as i) U pointwise collinear with xi ( in this case integral manifold distribution D totally geodesic or umbilic), ii) M has a constant xi-sectional curvature (under condition (or umbilic) isometric sphere S2n+1(pc) ra...