We propose a unified computational framework for the problem of deformation and rigidity of submanifolds in a homogeneous space under geometric constraint. A notion of 1-rigidity of a submanifold under admissible deformations is introduced. It measures how a deformation deviates from a one parameter family of motions u…
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48 results for “Deformation rigidity”
Rigidity of critical eigensections on spheres proven.
problem Rigidity of critical eigensections on spheres.
method Proved rigidity of critical eigensections through SO(3)-rotations.
result Minimal non-degenerate critical eigensections are deformation rigid.
Characterizes rigidity of compact foliations using deformations of Lie groupoids and algebroids.
problem Rigidity of compact foliations on manifolds.
method Combining stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids.
result Cohomological characterization for rigidity of compact foliations.
Einstein manifolds are rigid under certain metric deformations.
problem Characterizing Einstein manifolds that resist volume-preserving metric deformations.
method Various characterizations and constructions of mass-decreasing perturbations.
result Constructs mass-decreasing perturbations of specific metrics.
The paper derives Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
problem Computing curvature and geodesic curvature for surfaces and curves in affine and rigid motions groups.
method Defined deformed Schouten-Van Kampen connections, computed Gaussian curvature limits, and signed geodesic curvature.
result Derived Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
Locally connected deformation spaces for 3-manifolds.
problem Locating quasiconformally rigid points in hyperbolic 3-manifolds.
method Proving local connectedness at specific points in the deformation space.
result The deformation space is locally connected at quasiconformally rigid points.
In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations.
Study second-order obstruction to nearly structure deformations.
problem Proper nearly structure rigidity on Aloff-Wallach space.
method Second-order obstruction analysis, building on Alexandrov and Semmelmann work.
result Proves rigidity for nearly structure on .
Non-rigidity of hyperbolic manifold under scalar curvature constraints.
problem Non-rigidity of hyperbolic manifold under scalar curvature constraints.
method Compactly supported deformations, topological constraints.
result Non-rigidity under scalar curvature constraints, rigidity under topological constraints.
On the Rigidity of math.DG
Revisits Koiso's rigid metrics on complex projective spaces.
problem Computing obstructions to integrability of deformations.
method Elementary complex differential geometry.
result Computes Koiso's obstruction on .
Homotopy operators help describe structures in equivariant deformation problems.
problem Equivariant deformation problems in algebraic structures.
method Use homotopy operators for an -algebra associated with the problem.
result Smooth parametrization of the space of structures around a given one.
Rigidity of Fubini-Study metric on odd complex Grassmannians.
problem Characterize infinitesimal deformations of the Fubini-Study metric on complex Grassmannians.
method Explicit description of infinitesimal Einstein deformations, integration analysis.
result Fubini-Study metric on odd complex Grassmannians is rigid.
The study classifies nilpotent Lie foliations with cohomological obstructions.
problem Understanding rigidity of nilpotent Lie foliations under solvable deformations.
method Development of a cohomological framework and algebraic criterion for rigidity.
result Established a necessary and sufficient algebraic criterion for rigidity in generalized Heisenberg groups.
New examples of rigid Lie foliations with dense leaves found.
problem Infinitesimal rigidity of Lie foliations with dense leaves.
method Construction of specific Lie foliations.
result First examples of infinitesimally rigid Riemannian foliations with dense leaves.
Given a closed hyperbolic Riemannian surface, the aim of the present paper is to describe an explicit construction of smooth deformations of the hyperbolic metric into Finsler metrics that are not Riemannian and whose properties are such that the classical Riemannian results about entropy rigidity, marked length spectr…
New equations reveal moduli space rigidity in geometric deformations.
problem Understanding moduli space rigidity in geometric deformations.
method Coupled Hitchin-He equations, Lax pair, nonlinear embedding.
result Moduli space is analytically isomorphic to the classical case for small deformations.
Characterizes rigid and flexible hyperbolic cone metrics and billiards.
problem Understanding the rigidity and flexibility of hyperbolic cone metrics and their billiard dynamics.
method Characterization through Liouville currents and deformation spaces.
result Generic rigidity and parameterization of deformation spaces for flexible metrics.
Unlike Legendrian submanifolds, the deformation problem of coisotropic submanifolds can be obstructed. Starting from this observation, we single out in the contact setting the special class of integral coisotropic submanifolds as the direct generalization of Legendrian submanifolds for what concerns deformation and mod…
Study on scalar curvature deformations in pseudohermitian manifolds.
problem Deformation of scalar curvature in pseudohermitian manifolds.
method Analogy with Riemannian manifolds, introduction of -singular spaces, stability conditions, partial infinitesimal rigidity.
result Partial infinitesimal rigidity result for scalar curvature of compact pseudohermitian manifolds.
Study on deformations of LC Spin(7) instantons simplifies the problem.
problem Deformation theory of instantons on locally conformal Spin(7) manifolds.
method Reformulated linearized deformation equations using a t-parameter family of Dirac operators, demonstrating cancellation of torsion terms.
result The deformation space H^1 is governed by Levi-Civita geometry, reducing the problem to a torsion-free setting.
Study Kähler-Einstein edge metrics on Hirzebruch surfaces, verifying a conjecture and finding a rigid singularity.
problem Verifying a conjecture about Kähler-Einstein edge metrics on Hirzebruch surfaces.
method Using the Calabi ansatz, constructing a family of metrics and studying their angle deformation.
result Verification of a conjecture and finding a rigid singularity.
Hodge numbers of Sasakian manifolds remain unchanged under deformations.
problem Invariance of Hodge numbers under deformations of Sasakian manifolds.
method Analysis of deformations of Sasakian structures and use of transversely elliptic operators.
result Hodge numbers are invariant under arbitrary deformations of the Sasakian structure.
The thesis explores integrable systems and rigidity in PDEs with symmetry.
problem Understanding the deformation theory and rigidity of PDEs with symmetry.
method The approach involves studying completely integrable systems, their equivalence relations, and the deformation theory of PDEs with pseudogroups of symmetries.
result A solution is rigid if its deformation cohomology vanishes and certain estimates hold.
To a hyperbolic manifold one can associate a canonical projective structure and ask whether it can be deformed or not. In a cusped manifold, one can ask about the existence of deformations that are trivial on the boundary. We prove that if the canonical projective structure of a cusped manifold is infinitesimally proje…
Proves rigidity of geodesic balls in spheres under certain deformations.
problem Rigidity of geodesic balls in spheres under smooth deformations.
method Real Killing connection and solution of Dirac operator boundary value problem.
result Rigidity result for geodesic balls in spheres fails for hemispheres.
Study examines deformations of Kerr-(A)dS near horizon geometry.
problem Analyzing deformations of Kerr-(A)dS near horizon geometry.
method Two-part proof: elimination of Fourier modes and analyticity argument.
result No odd Fourier modes found for linear perturbations.
Study on complex Grassmannians' rigidity using Einstein deformations.
problem Characterizing integrable infinitesimal Einstein deformations of complex Grassmannians.
method Analyzing the integrability to second order of infinitesimal deformations using Koiso's obstruction polynomial.
result Characterized integrable deformations as an explicit variety in su(n), showing is isolated for odd n.
We formulate the deformation theory for instantons on nearly Kähler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group with the kernel of an elliptic operator, and prove that abelian instantons are rigid…
Study shows unique Einstein metrics on and related spaces.
problem Rigidity of Einstein metrics on and related spaces.
method Proof of rigidity using infinitesimal deformations and connections to Ricci flow.
result Bi-invariant Einstein metric on is isolated in the moduli space of Einstein metrics.
We study a notion of deformation for simplicial trees with group actions (G-trees). Here G is a fixed, arbitrary group. Two G-trees are related by a deformation if there is a finite sequence of collapse and expansion moves joining them. We show that this relation on the set of G-trees has several characterizations, in …
A new method for non-rigid point set registration reduces computational complexity.
problem Efficiently registering non-rigid point sets with large numbers of points.
method Structured Analytic Coherent Point Drift (Analytic-CPD) reformulates CPD for structured analytic mappings.
result Analytic-CPD reduces computational complexity by controlling the deformation model's dimensionality.
Study shows Einstein structures on 4-manifolds are rigid.
problem Rigidity of Einstein structures in four dimensions.
method Examined deformations of the round four-sphere and analyzed self-dual structure of Einstein manifolds.
result Any deviation from the standard metric of the round four-sphere breaks the Einstein condition.
We show that any compact orientable hyperbolic 3-cone-manifold with cone angle at most πcan be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local rigidity by Hodgson and Kerckhoff implies the global rigidity for compact orientable hype…
The study explores deformations of standard locally homogeneous spaces.
problem Understanding how discrete subgroups can be deformed while preserving proper discontinuity.
method Classification results for standard quotients, including local rigidity, deformation criteria, and Zariski-closure conditions.
result Conditions for local rigidity, deformation into nonstandard quotients, and maximal Zariski-closure of discontinuous groups.
The paper studies Einstein metrics on specific manifolds and their rigidity properties.
problem Investigating rigidity of Einstein metrics on homogeneous Gray manifolds.
method Computing coindex and analyzing infinitesimal deformations of Einstein metrics.
result Infinitesimal Einstein deformations on are not integrable.
This paper concerns with deformations of noncompact complex hyperbolic manifolds (with locally Bergman metric), varieties of discrete representations of their fundamental groups into and the problem of (quasiconformal) stability of deformations of such groups and manifolds in the sense of L.Bers and D.Sulliva…
The paper introduces flat grafting to deform quadratic differentials on surfaces.
problem Deforming quadratic differentials on surfaces of finite type.
method Flat grafting as a deformation analogous to the grafting map on hyperbolic surfaces.
result Characterizes cone point splitting deformations and proves rigidity properties.
We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms preserving the set of elliptic subgroups).
Compact hyperbolic complex manifolds are rigid under deformation.
problem Studying the deformation behavior of compact hyperbolic complex manifolds.
method Analyzing smooth families of compact complex manifolds over the unit disk and compact Riemann surfaces.
result The -locus is either at most a discrete subset or the whole domain, depending on the family structure.
Study on ALH manifolds with boundary, showing surjectivity of scalar curvature map and mass rigidity.
problem Characterizing ALH manifolds with boundary and their mass.
method Scalar curvature deformation analysis and mass rigidity study.
result ALH manifolds that minimize mass integrals are characterized.
Geometric structures modeled on smooth projective horospherical varieties of Picard number onemath.AG
Geometric structures on special manifolds are studied for rigidity.
problem Characterize and prove rigidity of geometric structures on rational homogeneous manifolds.
method Use Cartan geometry to study horospherical varieties and geometric structures modeled on them.
result Geometric structures on smooth projective horospherical varieties of Picard number one are locally equivalent to the standard structure.
Let M be an 8-manifold with a Spin(7)-structure. We first show that closed Cayley submanifolds of M form a smooth moduli space for a generic Spin(7)-structure. Then we study the deformations of a compact, connected Cayley submanifold X of M with non-empty boundary contained in a given submanifold W of M such that X and…
The paper examines deformations of pseudoholomorphic curves in a nearly Kähler sphere.
problem Investigating rigidity and deformability of pseudoholomorphic curves in .
method Analyzing moduli space of minimal surfaces isometric to pseudoholomorphic curves.
result Describes the moduli space of noncongruent minimal surfaces isometric to pseudoholomorphic curves.
A hypersurface without umbilics in the n+1 dimensional Euclidean space is known to be determined by the Moebius metric and the Moebius second fundamental form up to a Moebius transformation when n>2. In this paper we consider Moebius rigidity for hypersurfaces and deformations of a hypersurface preserving the Moebius m…
Using a hyperKähler rotation on complex structures of a Calabi-Yau 2-fold and rolling of an isotropic 2-submanifold in a symplectic 6-manifold, we construct, by gluing, a natural family of immersed Lagrangian deformations of a branched covering of a special Lagrangian 3-sphere in a Calabi-Yau 3-fold and study how they …
The Clifford torus is unstable but rigid in mean curvature flow.
problem Stability and rigidity of the Clifford torus in mean curvature flow.
method Analysis of higher order phenomena, including entropy minimisation and infinitesimal deformations.
result The Clifford torus is locally unique as a self-shrinker for mean curvature flow.
Researchers prove spectral rigidity of Liouville tori under specific conditions.
problem Spectral rigidity of Liouville tori under generic conformal classes.
method Noncancellation of wave trace and analysis of second order variational formula for energy.
result Laplace isospectral deformations of Liouville metrics on torus are trivial.
The paper studies rigidity and continuity in nonlinear elasticity on manifolds and hypersurfaces.
problem Rigidity and continuity properties of elastic bodies in non-Euclidean settings.
method Geometric rigidity estimates, asymptotic rigidity of elastic membranes, simplified geometric proof of continuous dependence.
result Established geometric rigidity estimate and proved asymptotic rigidity of elastic membranes.