Super McShane identitymath.GT
Authors derive McShane identity for super tori.
problem Deriving McShane identity for super tori.
method Super Teichmüller theory and supergeometry.
result Asymptotic growth rate of length spectra established.
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48 results for “super tori”
We prove that a constrained Willmore immersion of a 2-torus into the conformal 4-sphere is either of "finite type", that is, has a spectral curve of finite genus, or is of "holomorphic type" which means that it is super conformal or Euclidean minimal with planar ends. This implies that all constrained Willmore tori in …
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.
problem Unified extended super-symmetry and higher flux densities.
method Using super-Lie-infinity algebras and their extensions and cyclifications.
result Derivation of topological T-duality laws from super-Lie-infinity structure.
Study super cluster algebras from super Plücker and Ptolemy relations.
problem Developing super cluster algebra structure in super Grassmannians.
method Analyzing super Plücker and Ptolemy relations, developing super cluster structure.
result New simple form of super Plücker relations for $\Gr_{r|1}(n|1)$.
Super twisted productsmath.DG
The paper defines and analyzes curvature tensors on super twisted product spaces.
problem Investigating curvature tensors on super twisted product spaces.
method Defined -curvature tensor, computed curvature tensors and Ricci tensors, and studied curvature flatness.
result Mixed Ricci-flat super twisted product semi-Riemannian manifolds can be expressed as super warped product manifolds.
With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular representation is not super unitary. I will argue that weakening the definition of a super Hilbert space (by allowing the super scalar product to b…
We establish a higher generalization of super L-infinity-algebraic T-duality of super WZW-terms for super p-branes. In particular, we demonstrate spherical T-duality of super M5-branes propagating on exceptional-geometric 11d super spacetime.
This paper explores twisted Lagrangian tori in C^2 and their Hamiltonian stationarity.
problem Understanding the Hamiltonian stationarity of twisted Lagrangian tori in C^2.
method Investigation of differential geometry of twisted tori, including product and Chekanov's exotic tori.
result Only product tori are minimal under Hamiltonian deformations, indicating Chekanov's exotic tori are not area minimal.
Researchers create holographic super-embeddings for M5 and M2 branes.
problem No concrete examples of super-embeddings for M5 and M2 branes existed.
method Constructed explicit holographic super-embeddings of probe M5 and M2 branes into their super-AdS backgrounds.
result Explicit holographic super-embeddings of M5 and M2 branes were successfully constructed.
Develops Riemannian geometry for noncommutative super surfaces.
problem No specific problem stated; focuses on mathematical development.
method Introduces metric and connections on noncommutative super surfaces, showing compatibility and zero torsion under certain conditions.
result Noncommutative super surfaces have a well-defined Riemannian geometry with properties analogous to classical Riemannian geometry.
Defines super stable maps and proves quotient superorbifolds for genus zero.
problem Defines stable supercurves and super stable maps of genus zero.
method Uses labeled trees and slice theorem for super Lie groups.
result Proves moduli space of stable supercurves and super stable maps are quotient superorbifolds.
Smooth 2-tori in R^4 can be approximated by polyhedral Lagrangian or isotropic tori.
problem Approximating smooth 2-tori in high-dimensional spaces.
method Polyhedral approximation using Lagrangian and isotropic tori.
result Smooth 2-tori can be approximated by polyhedral Lagrangian or isotropic tori in C0 or C1 sense.
Defines semi-symmetric metric connection on super warped products.
problem Computing curvature and Ricci tensors on super warped products.
method Introduced semi-symmetric metric connection and conditions for Einstein spaces.
result Conditions for super warped product spaces to be Einstein with semi-symmetric metric connection.
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short intro…
New theorem disproves Angle Defect for super triangles.
problem Angle Defect Theorem for N=1 super hyperbolic geometry.
method Action of OSp(1|2) on real super Minkowski space and brute-force computation.
result Disproves Angle Defect Theorem and provides novel additive function.
Constructs the moduli space of super J-holomorphic curves.
problem Defines and constructs the moduli space of super J-holomorphic curves.
method Uses component fields of a super differential equation and a transversality argument.
result Constructs the moduli space of super J-holomorphic curves as a smooth subsupermanifold.
The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations of the Riemann surface and the gravitino. Furthermore the action functional of no…
The paper studies special warped products with a specific connection on super Riemannian manifolds.
problem Investigating curvature and Ricci tensors on super warped product spaces with a semi-symmetric non-metric connection.
method Defined a semi-symmetric non-metric connection, computed curvature and Ricci tensors, and introduced and analyzed two types of super warped product spaces.
result Conditions for two super warped product spaces with a semi-symmetric non-metric connection to be Einstein spaces are provided.
The paper classifies minimal immersions of flat 3- and 4-tori in spheres by their first eigenfunctions.
problem Classifying minimal immersions of flat 3- and 4-tori in spheres by their first eigenfunctions.
method General construction of homogeneous minimal flat n-tori in spheres, detailed investigations of shortest vectors in lattices.
result There exists a 2-parameter family of non-congruent λ1-minimal flat 4-tori.
Hopf tori and standard torimath.DG
Characterizes conformal classes of tori using differential geometry.
problem Classifying conformal classes of tori in complex dimension 1.
method Basic differential geometry methods, contrasting with Hopf tori.
result Complete characterization of conformal classes of product and standard flat tori.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
problem Extending symmetries of bihamiltonian hierarchies.
method Constructing super tau-covers for bihamiltonian integrable hierarchies.
result Symmetries of bihamiltonian hierarchies extended to super tau-covers.
We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Using a generalization of a Theorem of Rogers…
Study finds non-isotopic transverse tori in Engel manifolds.
problem Identifying distinct transverse tori in Engel manifolds.
method Constructing an infinite family of non-isotopic transverse tori, introducing a homological invariant.
result Found an infinite family of non-isotopic transverse tori that are smoothly isotopic.
A super Lie group is a group whose operations are mappings in the sense of Rogers. Thus the underlying supermanifold possesses an atlas whose transition functions are functions. Moreover the images of our charts are open subsets of a graded infinite-dimensional Banach space since our space of …
Defines a super analog of Plücker embedding for Grassmannian.
problem Generalizing Plücker embedding to super vector spaces with mixed parity.
method Combines super vector space and its parity-reversion to construct embedding.
result Proves the embedding is an isomorphism to a weighted projective space.
Unified solution to M-theory problems using super-exceptional geometry.
problem M-theory's Lagrangian construction, gauge field origin, and supersymmetric enhancement.
method Combining homotopy theory, supergeometry, and super-homotopy theory.
result Unified description of M-theory Lagrangians and emergence of gauge fields.
The paper develops a theory of -superrings and their superschemes.
problem Developing a theory for -superrings and superschemes.
method Proving an equivalence between categories of fair affine -superschemes and fair -superrings.
result A key equivalence between fair affine -superschemes and fair -superrings.
Characterizes super-replication prices in a financial market model.
problem Characterizing prices in a financial market model.
method Characterizes prices as the supremum of mono-prior super-replication prices through extreme priors and martingale measures.
result Super-replication prices are the supremum of mono-prior super-replication prices.
Scheme resolves super-brane topology via equivariant structures.
problem Topological issues in super-brane dynamics.
method Geometric scheme for Green-Schwarz cocycles, equivariant structures.
result Equivariant structures resolve super-brane topology.
Defines super projective modules and explores their properties.
problem Exploring the geometric-algebraic link in super geometry.
method Defined and explored super projective modules over supersmooth functions.
result Module of vector fields over a supersphere is a super projective module.
This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the "borderline" between classical and super differential geometry with respect to the…
Matrix formulas for super Teichmüller spaces generalize previous work and yield super λ-lengths.
problem Calculating super λ-lengths on bordered surfaces with marked points.
method Using holonomy matrices of elements in the supergroup OSp(1|2) to compute super λ-lengths in decorated super Teichmüller spaces.
result Matrix formulas for arcs on bordered surfaces yield super λ-lengths in Penner-Zeitlin's decorated super Teichmüller space.
3d Super Hyperbolic Geometrymath.GT
Extends Wigner's representation to study super hyperbolic geometry.
problem Understanding geometry in super hyperbolic three-space.
method Extended Wigner's representation of the Lorentz group to OSp_C(1|2) and applied to Minkowski (3,1|4)-dimensional super space.
result Proof of divergence of the volume of a typical ideal tetrahedron in super hyperbolic three-space.
Square-tiled torimath.GT
We study square-tiled tori, that is, tori obtained from a finite collection of unit squares by parallel side identifications. Square-tiled tori can be parametrized in a natural way that allows to count the number of square-tiled tori tiled by a given number of square tiles. There is a natural $\mathrm{SL}(2,\mathbf{Z})…
Extends differential geometry concepts to manifolds with super tangent bundles.
problem No specific problem stated; extending differential geometry to super tangent bundles.
method Introduces super tangent bundle and extends differential geometry concepts.
result Basic notions of differential geometry extended to manifolds with super tangent bundles.
New findings on isospectral tori and harmonic maps between flat tori.
problem Determining if isospectral tori are isometric using harmonic maps.
method Examined harmonic maps between flat tori, focusing on Milnor's isospectral tori.
result Milnor's isospectral tori cannot be distinguished by harmonic maps from lower-dimensional tori, but can be distinguished by higher-dimensional ones.
Stable 2-lobed Delaunay tori found in 3-sphere.
problem Stability of 2-lobed Delaunay tori in the 3-sphere.
method Constrained Willmore surfaces in the 3-sphere.
result 2-lobed Delaunay tori are stable.
Constructs flows of tori in sphere perturbations for Morse homology.
problem Understanding tori in sphere perturbations.
method Constructs eternal mean curvature flows of tori.
result Constructs flows of tori in sphere perturbations.
We prove that the conformal immersions of complex two tori into which locally minimize their conformal volume in their conformal class all satisfy some elliptic PDE. We prove that they are either minimal tori, CMC flat tori, elliptic conformally constrained minimal tori or critical point of the area under some fi…
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.
Constructs maps from field theories to complexified K-theory and elliptic cohomology.
problem Identifying geometric models for Chern characters in supersymmetric field theories.
method Higher-dimensional generalization of Fei Han's method, involving super moduli spaces and derived geometry.
result Provides evidence for the Stolz--Teichner program and geometric models for Chern characters.
Paper constructs super integrable systems on color Lie algebra.
problem Super integrable systems on color Lie algebra.
method Using non-isospectral problems with matrices from color Lie algebra , constructing (1+1)- and (2+1)-dimensional systems.
result Super integrable systems and their Hamiltonian structures constructed on color Lie algebra .
Researchers identify only two types of tori with specific energy constraints.
problem Finding constrained Willmore tori in 3-space with specific energy limits.
method Analyzing isothermic constrained Willmore tori in the 3-sphere.
result Homogeneous and 2-lobe Delaunay tori are the only isothermic constrained Willmore tori with Willmore energy below 8π.
Note on instabilities in super-time-stepping methods for Heston model.
problem Instabilities in super-time-stepping methods applied to Heston model.
method Exploration of explicit super-time-stepping schemes (RK-Chebyshev, RK-Legendre) for Heston model.
result Relevance of stability remarks beyond super-time-stepping schemes.
Study of critical tori for mean curvature energies in Killing submersions.
problem Analyzing surface energies in Killing submersions.
method Symmetry reduction and binormal evolution of critical curves.
result Construction of vertical tori critical for mean curvature energies.
The super or Z_2-graded Schouten-Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors Λof even order. The corresponding super `Jacobi identities' are expressed by stating that these tensors have zero…
Biharmonic tori in spheresmath.DG
We consider proper-biharmonic flat tori with constant mean curvature (CMC) in spheres and find necessary and sufficient conditions for certain rectangular tori and square tori to admit full CMC proper-biharmonic immersions in , as well as the explicit expressions of some of these immersions.
Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elasticamath.DG
Isothermic tori with one planar curvature line found and characterized.
problem Classifying isothermic tori with specific curvature lines.
method Complex analytic methods and explicit theta function formulas.
result Explicit formulas for family of plane curves and their relation to hyperbolic elastica.