Homogeneous Hypersurfaces Research Articles

A characterization of all homogeneous real hypersurfaces in a complex projective space by observing the extrinsic shape of geodesics

We will give a characterization of all homogeneous real hypersurfaces in a complex projective space by observing the extrinsic shape of geodesics with initial vectors lying in the maximal holomorphic subspace of the tangent space at each point.

Higher Weights of Anticodes and the Generalized Griesmer Bound

We show that the minimum r-weight dr of an anticode can be expressed in terms of the maximum r-weight of the corresponding code. As examples, we consider anticodes from homogeneous hypersurfaces (quadrics and Hermitian varieties). In a number of cases, all differences (except for one) of the weight hierarchy of such an anticode meet an analog of the generalized Griesmer bound.

Homogeneous hypersurfaces in hyperbolic spaces

Homogeneous hypersurfaces in hyperbolic spaces

Holomorphic rank of hypersurfaces with an isolated singularity

LetV be a germ at 0 ∈C2,n≥3, of hypersurface with an isolated singularity at 0. In this paper we prove that the maximal number of germs of vector fields inV*=V−0, which are linearly independent in all points ofV* is two. In the casesn=3,4 and of quasi homogeneous hypersurfaces (∀n≥3), we prove that this number is one.

The classification of naturally reductive homogeneous real hypersurfaces in complex projective space

We completely classify the naturally reductive homogeneous real hypersurfaces in a complex projective space. We conclude that only homogeneous real hypersurfaces of type (A) are naturally reductive.

Topology change in canonical quantum cosmology

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes.

Homogeneous real hypersurfaces in ℂ2

Homogeneous real hypersurfaces in ℂ2

Some invariants of tubular hypersurfaces in ℂ2

Holomorphic invariants of tubular hypersurfaces (tubes) over plane analytic curves are treated. Nonspherical Levi nondegenerate tubes over affine homogeneous curves are studied. Such surfaces are shown to be holomorphically equivalent if and only if they are affinely equivalent. Two problems concerning the description of locally specified homogeneous hypersurfaces in ℂ2 are posed.

Averages over homogeneous hypersurfaces in

Averages over homogeneous hypersurfaces in

Möbius geometry for hypersurfaces in S4

Our purpose in this paper is to study Möbius geometry for those hypersurfaces in S4 which have different principal curvatures at each point. We will give a complete local Möbius invariant system for such hypersurface in S4 which determines the hypersurface up to Möbius transformations. And we will classify the so-called Möbius homogeneous hypersurfaces in S4.

On negative weight derivations of the moduli algebras of weighted homogeneous hypersurface singularities

On negative weight derivations of the moduli algebras of weighted homogeneous hypersurface singularities

Cosmic Censorship for Some Spatially Homogeneous Cosmological Models

The global properties of spatially homogeneous cosmological models with collisionless matter are studied. It is shown that as long as the mean curvature of the hypersurfaces of homogeneity remains finite no singularity can occur in finite proper time as measured by observers whose worldlines are orthogonal to these hypersurfaces. Strong cosmic censorship is then proved for the Bianchi I, Bianchi IX, and Kantowski-Sachs symmetry classes.

The classification of 3-dimensional locally strongly convex homogeneous affine hypersurfaces

The classification of 3-dimensional locally strongly convex homogeneous affine hypersurfaces

The gravity of three-forms

Solutions of Einstein’s equations are examined when a particular class of closed three-form fields is taken as a source. The choice of source is motivated by developments in particle physics indicating the possible existence of physical fields described by three-forms. After summarizing basic dynamical equations and some properties, attention is focused on two particular configurations: (1) static, spherically symmetric, self-gravitating, three-form fields; and (2) homogeneous and isotropic geometries coupled to three-forms. For the spherically symmetric case, there exists two mutually exclusive sets of effective equations, solutions which describe static, spherically symmetric, self-gravitating axion fields. For the one class of the effective equations, a two-parameter family of asymptotically flat solutions of the Einstein axion field equations have been constructed. The axionic black hole solution of Bowick et al. [Phys. Rev. Lett. 61, 2823 (1988)] is also recovered as a special case of this class. For the other set of equations, only a special solution has been constructed. Its properties and global structure are discussed at length. For the case of axions coupled to homogeneous and isotropic geometries, explicit solutions of the relevant equations have also been constructed. In particular, for the case where the hypersurfaces of homogeneity are either flat or characterized by negative curvature, a global solution is obtained. It represents an ever expanding universe originating from a spacelike curvature singularity. For the case of a closed universe, local solutions have been constructed, which in principle can be patched to yield a global solution. Nevertheless, by employing them, the singularity structure of this solution was able to be analyzed. It behaves in the same manner as the previous two cases.

Infinitesimal CR automorphisms of rigid hypersurfaces in C2

In this paper, we describe the space of infinitesimal CR automorphisms of a rigid, real analytic, real hypersurface in C2. We use these results to obtain a geometric characterization of the homogeneous hypersurfaces. Here, a hypersurface is called homogeneous if it is equivalent to one given by an equation of the formIm(w) =p wherep is a homogeneous polynomial inz and\(\bar z\). This gives an answer in dimension 2 to a problem posed by Linda Rothschild. We give another answer, in terms of a normal form for the defining function, in our paper “A normal form for rigid hypersurfaces in C2.”

Stability of spatially homogeneous plane wave spacetimes. I

The problem of ascertaining the stability of a given spatially homogeneous solution of Einstein's equations to small metric perturbations was examined by Barrow and Sonoda (1986), and their method was discussed by Siklos (1988). In this paper, one of the points mentioned by Siklos is investigated further: the role of the constraint equation. It is shown that the constraint equation can lead to problems aside from those (e.g. linearization stability) usually considered. A particularly simple example is used to illustrate these points, namely the homogeneous vacuum plane wave metric, which for a certain range of values of its parameters admits spatially homogeneous hypersurfaces. One way of avoiding the problems associated with the constraint equation is simply to ignore it. In most cases, this will not affect the outcome.

Homogeneous hypersurfaces in Kähler C-spaces with b2=1

Homogeneous hypersurfaces in Kähler C-spaces with b2=1

Isotropy representations of semisimple symmetric spaces and homogeneous hypersurfaces

Isotropy representations of semisimple symmetric spaces and homogeneous hypersurfaces

Curvature homogeneous hypersurfaces immersed in a real space form

Curvature homogeneous hypersurfaces immersed in a real space form

Conformal Killing vectors in Robertson-Walker spacetimes

It is well known that Robertson-Walker spacetimes admit a conformal Killing vector normal to the spacelike homogeneous hypersurfaces. Because these spacetimes are conformally flat, there are a further eight conformal Killing vectors, which are neither normal nor tangent to the homogeneous hypersurfaces. The authors find these further conformal Killing vectors and the Lie algebra of the full G15 of conformal motions. Conditions on the metric scale factor are determined which reduce some of the conformal Killing vectors to homothetic Killing vectors or Killing vectors, allowing the authors to regain in a unified way the known special geometries. The non-normal conformal Killing vectors provide a counter-example to show that conformal motions do not, in general, map a fluid flow conformally. They also use these non-normal vectors to find the general solution of the null geodesic equation and photon Liouville equation.