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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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13 results for “3-tori”

Classification of Minimal Immersions of Conformally Flat

3

-Tori and

4

-Tori in Spheres by The First Eigenfunctionsmath.DG

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.

minimal immersions flat tori spheres first eigenfunctions spectral geometry

2022-12-05abs ↗pdf ↗

Nilpotent structures and collapsing Ricci-flat metrics on K3 surfacesmath.DG

Study on K3 surfaces with collapsing metrics and nilpotent structures.

problem Exploring Ricci-flat metrics on K3 surfaces that collapse.

method Continuous map from K3 surface to an interval, with specific fiber types.

result Bubbles of Tian-Yau and Taub-NUT metrics appear as fibers.

K3 surfaces Ricci-flat metrics collapsing nilpotent structures 3-tori

2018-07-24abs ↗pdf ↗

A compact

G_2

-calibrated manifold with first Betti number

b_1=1

math.DG

Researchers create a compact 7-manifold with unique $G_2$ structure and first Betti number 1.

problem Constructing a compact manifold with specific

G_2

structure properties.

method Constructing a formal 7-manifold with a closed

G_2

-structure and first Betti number 1, and demonstrating non-existence of torsion-free

G_2

structures.

result The construction of a compact manifold with a closed

G_2

-structure and first Betti number 1, which does not admit any torsion-free

G_2

-structure.

G2 structure compact manifold first Betti number torsion-free 7-manifold

2018-08-21abs ↗pdf ↗

A fully nonlinear "Generalised Monge-Ampère" PDE on a torusmath.DG

We prove an existence result for a "generalised" Monge-Ampère equation introduced earlier under some assumptions on a flat complex 3-torus. As an application we prove the existence of Chern connections on certain kinds of holomorphic vector bundles on complex 3-tori whose top Chern character forms are given representat…

2013-10-07abs ↗pdf ↗

A new obstruction for ribbon-moves of 2-knots: 2-knots fibred by the punctured 3-tori and 2-knots bounded by homology spheresmath.GT

This paper gives a new obstruction for ribbon-move equivalence of 2-knots. Let $K$ and $K'$ be 2-knots. Let $K$ and $K'$ are ribbon-move equivalent. One corollary to our main theorem is as follows. A 2-dimensional fibered knot whose fiber is the punctured 3-dimensional torus is not ribbon-move equivalent to any 2-dimen…

2010-03-12abs ↗pdf ↗

Lagrangian torus invariants using ECH = SWFmath.SG

Constructs invariants from Lagrangian tori in symplectic 4-manifolds.

problem Tackles invariants of Lagrangian tori in symplectic 4-manifolds.

method Uses ECH and monopole Floer homology to construct distinguished elements.

result Repackages Gromov and Seiberg-Witten invariants of torus surgeries.

Lagrangian tori symplectic 4-manifolds embedded contact homology monopole Floer homology Gromov invariants

2019-10-08abs ↗pdf ↗

Decomposition of Lagrangian classes on K3 surfacesmath.DG

Study decomposability of Lagrangian classes on K3 surfaces.

problem Decomposability of Lagrangian classes on K3 surfaces.

method Lattice theory and special Lagrangian submanifolds.

result Prove decomposability of Kähler classes on dense subsets of the Kähler cone.

K3 surfaces Lagrangian classes special Lagrangian submanifolds Kähler cone dense subsets

2020-01-01abs ↗pdf ↗

Rohlin's invariant and gauge theory, I. Homology 3-torimath.GT

This is the first in a series of papers exploring the relationship between the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of a 3-manifold with the integral homology of a torus, given by counting projectively flat connections. We show that its mod 2 evaluation is given by the triple cup prod…

2003-02-11abs ↗pdf ↗

Gromov-Hausdorff stability of tori under Ricci and integral scalar curvature boundsmath.DG

New theorem on flat tori stability using harmonic maps and Ricci flow.

problem Stability of flat tori under Ricci and scalar curvature bounds.

method Harmonic map heat flow, Ricci flow, and RCD theories.

result Gromov-Hausdorff stability theorem for flat 3-tori.

flat tori Gromov-Hausdorff stability harmonic maps Ricci flow integral scalar curvature

2023-11-02abs ↗pdf ↗

The Ricci Curvature for Noncommutative Three Torimath.QA

Researchers compute Ricci curvature on noncommutative 3-tori.

problem Calculating Ricci curvature on noncommutative spaces.

method Used Connes' pseudodifferential calculus and localized spectral zeta functions.

result Explicitly computed Ricci curvature and scalar curvatures.

Ricci curvature noncommutative tori heat kernel spectral zeta functions scalar curvature

2018-08-09abs ↗pdf ↗

On the Equivalence Problem for Toric Contact Structures on S^3-bundles over S^2$math.SG

We study the contact equivalence problem for toric contact structures on $S^3$ -bundles over $S^2$ . That is, given two toric contact structures, one can ask the question: when are they equivalent as contact structures while inequivalent as toric contact structures? In general this appears to be a difficult problem. To f…

2012-04-10abs ↗pdf ↗

A New CR Invariant for Contact 3-Manifolds and Classes of Open Booksmath.GT

New invariant distinguishes tight contact structures on 3-tori.

problem Distinguishing tight contact structures on 3-manifolds.

method Introduced a new CR invariant

μ_M(ξ)

for co-oriented contact structures on 3-manifolds.

result First Chern classes of two tight contact structures on 3-torus are different.

contact structures 3-manifolds CR invariants open books 3-torus

2026-06-18abs ↗pdf ↗

Singularities of special Lagrangian fibrations and the SYZ Conjecturemath.DG

The SYZ Conjecture explains Mirror Symmetry between mirror Calabi-Yau 3-folds M,M' in terms of special Lagrangian fibrations f : M --> B and f' : M' --> B over the same base B, whose fibres are dual 3-tori, except for singular fibres. One of the main problems in proving the SYZ Conjecture (or even in finding the right …

2000-11-22abs ↗pdf ↗