We give a formula to calculate the indices of special (non-totally geodesic) minimal orbits of Hermann actions. Also, we give examples of such minimal orbits of Hermann actions and calculate their indices by using the formula.
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48 results for “action minimizing orbits”
Study on actions on symmetric spaces, focusing on orbit properties.
problem Investigating properties of orbits in symmetric spaces related to .
method Classification and analysis of orbits as Riemannian submanifolds, focusing on principal curvatures and specific types of orbits.
result Classification and properties of orbits in symmetric spaces related to .
We give examples of certain kind of minimal orbits of Hermann actions and discuss whether each of the examples is austere.
New orbits found in Lagrangian systems on surfaces.
problem Finding action minimizing periodic orbits in Tonelli Lagrangian systems.
method Analyzing minimal boundaries and using graph theorems.
result Existence of action minimizing simple periodic orbits.
Study minimal Lagrangian tori on Kähler manifolds, answering questions about their existence and stability.
problem Characterize minimal Lagrangian tori on Kähler manifolds.
method Investigate orbits of torus actions, analyze stability, and relate to ambient geometry.
result Partial answers to questions about minimal Lagrangian tori existence and stability.
Minimal action of mapping class group on character variety.
problem Character variety of Deroin-Tholozan representations.
method Geometric perspective using symplectic structure.
result Infinite mapping class group orbits are dense.
Ellipsoids host infinitely many minimal tori, bifurcating from a 2-torus orbit.
problem Minimal tori in ellipsoids.
method Analyzing 3D ellipsoids invariant under a 2-torus action.
result Infinitely many distinct minimal tori bifurcate from a 2-torus orbit.
The paper studies mean curvature flows on specific orbits of Hermann actions.
problem Analyzing mean curvature flows on principal orbits of Hermann actions.
method Using Mathematica to illustrate and calculate the flows and orbits.
result The minimal principal orbit's position is calculated and illustrated.
We introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like Yang-Mills and string theory and which generalise finite dimensional Riemannian principal fibre bundles induced by an isometric action. We show that the orbits of regulari…
The study constructs K-contact manifolds with minimal closed Reeb orbits and provides conditions for their homeomorphism to spheres.
problem Understanding K-contact manifolds with minimal closed Reeb orbits and their homeomorphism properties.
method Using Boothby-Wang fibration and Hamiltonian torus actions, the study constructs and analyzes K-contact manifolds.
result The existence of K-contact manifolds with minimal closed Reeb orbits that are not homeomorphic to spheres and have unique cohomology rings.
The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closedmath.SG
The paper characterizes contact 3-manifolds with closed Reeb orbits.
problem Characterizing contact 3-manifolds with closed Reeb orbits.
method Analyzing the action spectrum and minimal periods of Reeb orbits.
result A contact form with an action spectrum of rank 1 is uniquely determined by the minimal periods of its closed Reeb orbits.
We compute the Euler-Poincaré characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold.
Minimal orbits of semi-simple Lie groups are studied and related to invariant subspaces.
problem Characterizing minimal orbits of semi-simple Lie groups.
method Analyzing projective orbits induced by representations of semi-simple Lie groups and relating them to invariant subspaces of the underlying modules.
result Minimal orbits of semi-simple Lie groups are in bijection with minimal orbits of compact subgroups on invariant subspaces.
Study rigidifies Einstein manifolds with symmetry, proving conjecture.
problem Einstein manifolds with negative scalar curvature and Lie group action.
method Rigidity result for nilradical action and minimal Einstein submanifolds.
result Alekseevskii conjecture proven for negative scalar curvature homogeneous manifolds.
All principal orbits of the standard Hamiltonian -action on the complex projective space are Lagrangian tori.In this article, we prove that most of them are not volume minimizing under Hamiltonian isotopies of if the complex dimension is greater than two, although they are Ham…
Let $Φ\colon \sbat \times M \to M$ be a smooth action of the unit circle $ \sbat$ on a manifold . In this work, we compute the minimal model of in terms of the orbit space and the fixed point set , as a dg-module over the Sullivan's minimal model of .
Study of actions on curved manifolds with boundary results in new geometric invariant.
problem Classifying actions of compact Lie groups on curved manifolds with boundary.
method Introduced a new geometric invariant for compact symmetric spaces.
result List of representations of compact simple Lie groups with non-trivial reductions.
New proof shows almost all surface group actions are dense.
problem Transitivity of normal subgroups on character varieties.
method Proved almost minimal action of non-trivial normal subgroups.
result Almost all points in character variety have dense orbits.
Simultaneous Laminationsmath.GT
Study of laminations for pseudo-Anosov flows on three-manifolds.
problem Understanding laminations for pseudo-Anosov flows on three-manifolds.
method Analyzing laminations for pseudo-Anosov orbit space universal circles, using prelaminations and results from Barthelmé, Bonatti, and Mann.
result Laminations and are completely determined by prelaminations on the boundary of the orbit space.
Collapse of the mean curvature flow for certain kind of invariant hypersurfaces in a Hilbert spacemath.DG
In this paper, we investigate the regularized mean curvature flow starting from an invariant hypersurface in a Hilbert space equipped with an isometric and almost free action of a Hilbert Lie group whose orbits are regularized minimal. We prove that, if the invariant hypersurface satisfies a certain kind of horizontall…
Study properties of orbits of Hermann actions without commutability assumptions.
problem Investigate geometric properties of orbits of Hermann actions.
method Compute the second fundamental form and provide conditions for weak reflection and aridity.
result Sufficient conditions for weak reflection and aridity of orbits of Hermann action.
The paper proves the existence of minimal surfaces on certain manifolds.
problem Existence of minimal surfaces on manifolds with specific symmetries.
method Developed a regularity theory for equivariant Allen--Cahn solutions, showing convergence to minimal hypersurfaces.
result Closed Riemannian manifolds with cohomogeneity 2 and no exceptional orbits admit minimal hypersurfaces with optimal regularity.
The paper introduces austere and arid submanifolds in Hilbert spaces.
problem Classifying minimal orbits in hyperpolar PF actions on Hilbert spaces.
method Introducing austere and arid submanifolds into PF submanifolds in Hilbert spaces.
result Examples of infinite dimensional austere and arid PF submanifolds in Hilbert spaces.
We investigate the equivariant cohomology of the natural torus action on a K-contact manifold and its relation to the topology of the Reeb flow. Using the contact moment map, we show that the equivariant cohomology of this action is Cohen-Macaulay, which is a generalization of equivariant formality for torus actions wi…
Circle actions yield different orbit spaces.
problem Understanding differential structures on orbit spaces.
method Analyzing non-isomorphic linear circle actions.
result Non-diffeomorphic orbit spaces from different actions.
Let be a weakly reducible, unstabilized, Heegaard splitting of genus at least three in an orientable, irreducible -manifold . Then naturally acts on the disk complex as a group action. In this article, we prove if is topologically minimal and its topol…
This paper classifies geodesic orbit metrics on compact Lie group .
problem Classifying geodesic orbit metrics on compact Lie groups.
method Using representation theory of Lie subgroups, specifically weakly regular subgroups.
result Left-invariant geodesic orbit metrics on compact Lie group are classified.
Classifies actions on Minkowski space up to orbit equivalence.
problem Classifying actions on Minkowski space up to orbit equivalence.
method Classifying actions up to orbit equivalence, providing representations and orbit spaces.
result Orbits and orbit spaces determined for proper actions.
The paper examines Hamiltonian stability of Lagrangian tori in complex hyperbolic spaces.
problem Investigating Hamiltonian stability of Lagrangian tori in complex hyperbolic spaces.
method Standard Hamiltonian -action on ; proving stability and rigidity results.
result Existence of infinitely many H-unstable -orbits when .
The study proves conditions for symplectic torus actions on manifolds with non-contractible orbits.
problem Conditions for symplectic torus actions with non-contractible orbits.
method Analyzes symplectic torus actions on manifolds, proving conditions for Hamiltonian actions and orbit properties.
result Symplectic actions with non-contractible orbits are not Hamiltonian unless the orbits are contractible.
In this paper, we study the regularized mean curvature flow starting from invariant hypersurfaces in a Hilbert space equipped with an isometric almost free Hilbert Lie group action whose orbits are minimal regularizable submanifolds, where "almost free" means that the stabilizers of the group action are finite. First w…
Study shows mean action of periodic orbits in annuli is bounded by their Calabi invariant.
problem Understanding the average distortion of periodic orbits in area-preserving annuli.
method Analyzes action functions and Calabi invariants of diffeomorphisms near annulus boundaries.
result Infimum of mean action of periodic orbits is bounded by their Calabi invariant.
Formula calculates equivariant LS-category of symplectic toric manifolds.
problem Estimating the number of critical points in equivariant settings.
method Localization formula for equivariant LS-category.
result Equivariant LS-category equals number of fixed points for symplectic toric manifolds.
We study isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on the Minkowski space whose orbit spaces are non-Hausdorff. We show that there exist isometric cohomogeneity one actions on the Minkowski space which ar…
Reconstruct flows from their orbit spaces using group actions.
problem Reconstructing flows from their orbit spaces.
method Using group actions and pseudo-Anosov flows.
result Reconstruct flows from their orbit spaces.
No exceptional orbits found in Hilbert spaces actions.
problem Proving the non-existence of exceptional orbits in Hilbert spaces.
method Analyzing polar actions on separable Hilbert spaces by connected Lie groups.
result Proved non-existence of exceptional orbits in Hilbert spaces.
Classifies polar actions on 3D homogeneous spaces.
problem Classifying polar isometric actions on 3D homogeneous spaces.
method Orbit equivalence classification and study of cohomogeneity one actions.
result Classification of extrinsically homogeneous surfaces and orbit foliations.
In this paper we use structure preserving torus actions on Kahler-Einstein manifolds to construct minimal Lagrangian submanifolds. Our main result is: Let N^2n be a Kahler-Einstein manifold with positive scalar curvature with an effective T^n-action. Then precisely one regular orbit L of the T-action is a minimal Lagra…
The paper analyzes orbits of integer tuples using braid diagrams.
problem Determining orbits of integer tuples under braid diagram actions.
method Monoid action of braid diagrams on integer tuples.
result Orbits of integer tuples under up-down action of braid diagrams.
Classifies actions on complex space forms with Lagrangian orbits.
problem Classifying actions on complex space forms with Lagrangian orbits.
method Classifies holomorphic isometric actions on complex space forms.
result Only examples are Lagrangian affine subspace foliations of complex Euclidean spaces and Lagrangian horocycle foliations of complex hyperbolic spaces.
Highly curved orbit spacesmath.DG
Study on orbit spaces with curvature bounds.
problem Understanding the curvature bounds of orbit spaces.
method Analyzing isometric actions on unit spheres.
result The infimum of sectional curvatures is 1 for most actions.
Classifies pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
problem Classifying pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
method Generalized Anosov-like actions on bifoliated planes, ideal boundary analysis.
result Pseudo-Anosov flows on 3-manifolds are determined up to orbit equivalence by their ideal boundary actions.
Smooth approximations for continuous functions on orbit spaces.
problem Approximating continuous functions on orbit spaces.
method Study of subcartesian spaces and proper Lie group actions.
result Continuous functions can be approximated by smooth functions.
The notion of a complex hyperpolar action on a symmetric space of non-compact type has recently been introduced as counterpart of a hyperpolar action on a symmetric space of compact type. In this paper, we construct examples of a complex hyperpolar action without singular orbit and investigate the geometry of the orbit…
Study of geodesics on Riemannian stacks, measuring distances on orbit spaces.
problem Extending Riemannian geometry to singular spaces.
method Introduce stacky metrics and study stacky curves and geodesics on Riemannian stacks.
result Establish a stacky version of Hopf-Rinow Theorem.
Inequalities found in contact and symplectic geometry.
problem Finding inequalities in contact and symplectic geometry.
method Proving inequalities for Zoll contact and odd-symplectic forms.
result Proves a local systolic-diastolic inequality for Zoll contact and odd-symplectic forms.
We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of Kedra-Kotschick-Morita for this class of manifolds.
We investigate the submanifold geometry of the orbits of Hermann actions on Riemannian symmetric spaces. After proving that the curvature and shape operators of these orbits commute, we calculate the eigenvalues of the shape operators in terms of the restricted roots. As applications, we get a formula for the volumes o…