An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold is an affine manifold with holonomy consisting of affine transformati…
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14 results for “radiant”
Conelike radiant structuresmath.DG
Develops radiant structures for statistical manifolds.
problem Statistical manifolds with radiant vector fields.
method Formulates Einstein equations for special statistical structures.
result Conelike radiant structures exist and have canonical normalizations.
Locally conformally Hessian manifolds are dense in radiant ones of rank 1.
problem Characterizing locally conformally Hessian manifolds and their properties.
method Analyzing quotient spaces of Hessian manifolds and using statistical manifold theory.
result The set of radiant l.c.H. metrics of rank 1 is dense in all radiant l.c.H. metrics.
A selfsimiar manifold is a Riemannian manifold endowed with a homothetic vector field . We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian ma…
Given any smooth plane curve α(s)representing a mirror that reflects light the usual way and any radiant light source at a point in the plane, the reflected light will produce a caustic envelope. For such an envelope, we show that there is an associated curve \b{eta}(s) and a family of circles C(s) that roll on \b{eta}…
The paper studies the non-discrete automorphisms of projective manifolds.
problem Analyzing non-discrete automorphisms of projective manifolds.
method Applying results from [13] and Benzekri's functor to study topological properties.
result Orbits of the connected component of automorphisms are immersed projective submanifolds.
A Sim(n-1,1) affine manifold is an affine manifold whose linear holonomy is contained in the similarity lorentzian group but not in the lorentzian group. The class of similarity lorentzian affine manifolds is a small part in the nice class of conformally lorentzian flat manifolds. In this paper we show that a compact S…
The Margulis invariant is a function defined on a group of Lorentzian transformations acting on Minkowski space , that contains no elliptic elements. The spectrum of is the sequence of values of the Margulis invariant for all its elements. If the underlying linear group of is fixed, Drumm and Gold…
The study examines nilpotent similarity structures on manifolds and their properties.
problem Characterizing closed manifolds with nilpotent similarity structures.
method Generalizes convexity arguments to geodesic segments in nilpotent Lie groups.
result Closed manifolds with nilpotent similarity structures are either complete or radiant.
Study reveals flatness of Hessian metrics with non-negative Ricci curvature on foliation leaves.
problem Rigidity of Ricci curvature on Hessian manifold leaves.
method Analysis of Ricci curvature properties of Hessian metrics on foliation leaves.
result Non-negative Ricci curvature on a single leaf forces the Hessian metric to be flat and yields bounds on the first Betti number.
Paper proves certain closed affine manifolds without invariant lines don't exist.
problem Proving non-existence of closed affine manifolds with invariant lines.
method Developing map, holonomy, invariant line, large open subsets, modified proof.
result Developing image cannot meet invariant line if affine holonomy acts purely by translations.
We try to understand the geometric properties of -manifolds () with geometric structures modeled on $(\bR P^n, \PGL(n+1, \bR))$, i.e., -manifolds with projectively flat torsion free affine connections. We define the notion of -convexity of such manifolds due to Carriére for integers , $1 \leq i \le…
We present a technique for efficiently synthesizing images of atmospheric clouds using a combination of Monte Carlo integration and neural networks. The intricacies of Lorenz-Mie scattering and the high albedo of cloud-forming aerosols make rendering of clouds---e.g. the characteristic silverlining and the "whiteness" …
New method proves Alexandrov theorem for curved spacetimes.
problem Proving Alexandrov theorem for curved surfaces with conical singularities.
method Adapting Volkov's variational method to handle Lorentzian angles.
result Existence of a locally Minkowski 3-manifold with conical singularities isometric to a given surface.