Rigidity through a Projective Lens

Scattering and Lens Rigidity

Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results about lens rigidity but very little is known for scattering rigidity. We wil...

Boundary and Lens Rigidity of Finite Quotients

We consider compact Riemannian manifolds (M,∂M, g) with boundary ∂M and metric g on which a finite group Γ acts freely. We determine the extent to which certain rigidity properties of (M,∂M, g) descend to the quotient (M/Γ, ∂/Γ, g). In particular, we show by example that if (M,∂M, g) is boundary rigid then (M/Γ, ∂/Γ, g) need not be. On the other hand, lens rigidity of (M,∂M, g) does pass to the...

Boundary and Lens Rigidity of Lorentzian Surfaces

LARS ANDERSSON, MATTIAS DAHL, AND RALPH HOWARD Abstract. Let g be a Lorentzian metric on the plane R2 that agrees with the standard metric g0 = −dx + dy outside a compact set and so that there are no conjugate points along any time-like geodesic of (R2 , g). Then (R2 , g) and (R2 , g0) are isometric. Further, if (M, g) and (M∗, g∗) are two dimensional compact time oriented Lorentzian manifolds ...

The Rigidity of Families of Projective Calabi-yau Manifolds

In this paper, author studies the rigidity of the family of Calabi-Yau manifolds via the main tools: Variation of Hodge Structure and Higgs bundle. He Shows that some important families are rigid,for example : Lefschetz pencils of odd dimensional Calabi-Yau manifolds are rigid; Strong degenerated families are rigid;the families of CY manifolds admitting a degeneration with maximal unipotent mon...

Perceptual rigidity in paranoid schizophrenia: use of projective animal drawings.