Expanding on previous work, this note generalizes geometric structures results.
problem Generalizing geometric structures results.
method Generalization to a class of geometric structures including integrable almost-complex structures.
result Main results generalized to a broader class of geometric structures.
Unified approach to geometric structure equivalence problem.
problem Equivalence problem of geometric structures.
method Unified framework, step prolongation, structure function γ. result Unified scheme for equivalence problem of geometric structures.
Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to quasihomogeneous varieties, we first study horospherical varieties and geometric st…
Extends geometric structures to manifolds with new operators.
problem No specific problem stated; extending geometric structures.
method Defines new gradient and Laplace operators on manifolds with geometric structures.
result Provides properties of the new operators.
Defines structure constants for specific geometric structures on Lie groups.
problem No specific problem stated; focuses on defining structure constants.
method Not explicitly detailed in the abstract.
result Defines structure constants for almost complex, almost symplectic, and Riemannian structures on a local Lie group.
Paper connects geometric structures to algebra in high dimensions.
problem Understanding geometric structures in high dimensions.
method Relating minimal left ideals on Clifford algebras to geometric structures.
result Established a connection between algebraic and geometric properties.
The paper introduces geometric surgeries for flag structures and provides examples of uniformizable and non-uniformizable types.
problem Understanding and classifying flag structures of different types.
method Introducing geometric surgeries for flag structures and applying them to examples.
result Examples of both uniformizable and non-uniformizable flag structures were provided.
Geometric compactification for complex structures on Lie groups.
problem Compactifying moduli stack of complex structures on Lie groups.
method Describes a geometric compactification using CR structures transverse to a real foliation.
result Extra points represent CR structures transverse to a real foliation.
The paper studies geometric structures in Sol_3 with two connections.
problem Analyzing geometric structures in Sol_3 using specific connections.
method Used Levi-Civita and semi-symmetric non-metric connections to study Sol_3.
result Concluded geometric structures in Sol_3 with both connections.
A complex orthogonal (geometric) structure on a complex manifold is a geometric structure locally modelled on a non-degenerate quadric. One of the first examples of such a structure on a compact manifold of dimension three was constructed by Guillot. In this paper, we show that the same manifold carries a family of uni…
We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The…
The paper extends classical Darboux theorems to various geometric structures in field theories.
problem Extending classical Darboux theorems to new geometric structures.
method Exploring flat connections and polarizations for geometric structures.
result New Darboux theorems for various geometric structures in field theories.
Karigiannis discusses geometric flows of G2-structures, focusing on existence and uniqueness.
problem Existence and uniqueness of geometric flows of G2-structures.
method Introduced geometric structures, geometric flows, and discussed qualitative features. Focused on Ricci flow and DeTurck trick, then extended to G2-structures.
result Clarified conditions for short-time existence and uniqueness of G2-Laplacian flow.
Study geometric structures on LVM threefolds, focusing on resonant structures.
problem Understanding deformations of geometric structures on LVM threefolds.
method Using the Ehresmann-Thurston principle and Kuranishi family construction.
result Construction of a family containing all LVM threefolds and complete at every point.
Geometric cohomology model uses co-oriented maps to define a product structure.
problem Constructing a geometric model for cohomology of smooth manifolds.
method Develops a cochain complex model based on co-oriented smooth maps, focusing on their pull-back product structure.
result Geometric cochains with a partially defined product structure induce the cup product in cohomology.
New framework tackles geometric structure existence and classification.
problem Existence and classification of geometric structures.
method Developed a new framework of relative algebroids.
result New framework addresses geometric structure problems.
New geometric structures defined on SPD matrices for better understanding.
problem Understanding SPD matrices and their geometric properties.
method Introducing Finslerian and dual information-geometric structures on James' bicone domain.
result Geodesics correspond to straight lines in coordinate systems, and new dissimilarities generalize existing ones.
New proofs for complex Hopf manifolds using geometric structures.
problem Proving properties of complex Hopf manifolds.
method Constructing integrable holomorphic G-structures and flat holomorphic Cartan geometries.
result Provided a new proof of flat holomorphic Cartan geometries on complex Hopf manifolds.
Study the structure of equidistant decompositions in manifolds.
problem Geometric and topological structure of equidistant decompositions.
method Investigation of Riemannian manifolds.
result Detailed understanding of equidistant decompositions.
The paper explores geometric structures on Weil bundles and their canonical lifts.
problem Transfer of geometric structures from a manifold to its Weil bundle.
method Utilizes differential geometric properties and Weil projection to lift structures.
result Demonstrates canonical lifts of various geometric structures to Weil bundles.
New theory connects geometry without relying on connections.
problem Developing geometric structures without connections.
method Proposed alternative approach to Lie groups and geometric structures.
result Geometric structures can be developed independently of connections.
Geometric deformations preserve post-Lie algebra structure in regularity structures.
problem Deriving geometric deformations of post-Lie algebras.
method Extending geometrical notions of torsion and curvature, deriving compatibility conditions.
result Derives a pre-Lie structure for regularity structures, isomorphic to a post-Lie algebra.
We say that a germ G of a geometric structure can be transplanted into a manifold M if there is a suitable geometric structure on M which agrees with G on a neighborhood of some point P of M. We show for a wide variety of geometric structures that this transplantation is always possible provided that M does in fact adm…
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit description. This allows us to describe the structure of symmetric geometric structur…
Introduces VB-structures for geometric objects on manifolds.
problem Properties of higher tangent lifts of geometric structures.
method Introduces weighted structures for various geometric objects on a manifold with a homogeneity structure.
result Proves interesting properties of various weighted structures.
Geometric vector perceptrons improve protein structure learning.
problem Learning from protein structure with efficient and natural representations.
method Introducing geometric vector perceptrons to extend dense layers for Euclidean vectors, integrating geometric and relational reasoning.
result Improves model quality assessment and computational protein design over existing methods.
Defines contact structures on Heisenberg groups for geometric interpretation.
problem Finding a geometric interpretation for the Yamabe equation on Heisenberg groups.
method Defines contact structures of Heisenberg type, introduces a natural connection, and computes conformal scalar curvature.
result Establishes equivalence between contact Riemannian manifolds and contact structures of Heisenberg type.
We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show that under the usual regularizations, non-probabilistic methods cannot recover the differential geometric structure, but instead find mostl…
The study finds many tight contact structures on hyperbolic 3-spheres.
problem Finding tight contact structures on hyperbolic 3-spheres.
method Constructing hyperbolic homology 3-spheres and analyzing their tight contact structures.
result Produces hyperbolic homology 3-spheres with multiple distinct tight contact structures.
Geometric structures help in understanding thermodynamics.
problem Understanding thermodynamic systems using geometric methods.
method Using almost cosymplectic structures and variational arguments.
result Evolution equations are derived and discussed.
Geometric framework for SPD matrices preserving subspace structures.
problem Processing SPD-valued data with preserved subspace structures.
method Thompson geometry of the semidefinite cone, extreme generalized eigenvalues, geodesic space structure.
result Novel inductive mean of SPD matrices based on Thompson geometry.
Some geometric structures with associated Riemannian metrics have been considered in the book.
Geometric structures on 5-manifolds from surface group representations of G2'.
problem Constructing geometric structures on 5-manifolds from G2'-surface group representations.
method Using Higgs bundles and partial flag manifolds of G2' to construct geometric structures.
result Developing maps of geometric structures are the domain of discontinuity.
Introduces string structures linking to loop spaces.
problem Understanding geometric string structures.
method Explains connections to loop spaces.
result String structures linked to loop spaces.
Holomorphic structures on Oeljeklaus-Toma manifolds are shown to be locally homogeneous.
problem Characterizing holomorphic structures on Oeljeklaus-Toma manifolds.
method Proving local homogeneity for various holomorphic geometric structures.
result Holomorphic geometric structures on Oeljeklaus-Toma manifolds are locally homogeneous.
Geometric structures over algebras describe geodesics and spaces.
problem Understanding geodesics in hyperbolic and Euclidean spaces over non-standard algebras.
method Study geometric structures from Hermitian forms on real algebras (dual numbers, split-complex, split-quaternions).
result Presented a projective model for the hyperbolic bidisc.
Study on projective structures linked to Hitchin representations.
problem Understanding the topology and geometric properties of projective structures.
method Using gauge theory, flat bundles, Higgs bundles, and geometric constructions.
result Some projective structures are fibered in a standard way.
GCML preserves geometric structure in manifold clustering for diverse data types.
problem Loss functions in manifold clustering can corrupt latent space structure.
method GCML framework with isometric and ranking losses for geometric structure preservation.
result GCML outperforms other methods in latent space structure preservation and performance metrics.
Geometric quantization for specific symplectic structures proved.
problem Quantization of specific symplectic structures.
method Geometric quantization for constant rank presymplectic structures with Riemannian null foliation.
result Quantization-commutes-with-reduction theorem proved in this context.
Study geometric structures and their interactions under different metrics.
problem Understanding interactions between geometric structures under various metrics.
method Analyzing generalized polynomial structures and their behavior under different metrics on the generalized tangent bundle.
result Showed the commutation or anti-commutation of generalized polynomial structures forming triple structures.
Equivariant networks improve geometric prediction without scalar approximations.
problem Efficiently predicting geometric tensors in real-world scenarios.
method Equivariant networks for geometric prediction.
result Equivariant networks can generalize to unseen systems for geometric prediction.
Study geometric quantization on K3 surfaces, showing spectral convergence.
problem Quantization of K3 surfaces from spectral perspective.
method Special Lagrangian fibrations and hyper-Kähler structures.
result Spectral convergence of ∂ˉ-Laplacians on prequantum line bundles. Study on non-Kähler Calabi-Yau manifolds and their geometric structures.
problem Holomorphic geometric structures on non-Kähler compact complex manifolds.
method Beauville-Bogomolov decomposition and weak Bochner principle.
result Rigidity of Vaisman Calabi-Yau manifolds implies they are Kodaira manifolds.
The paper provides examples of geometric transitions in low dimensions.
problem Exploring geometric transitions between different types of structures in low dimensions.
method Explicit examples and computations of transitions from hyperbolic to Euclidean, spherical, and Anti-de Sitter structures.
result Details of elementary computations and techniques are provided to explain geometric transitions.
Study geometric structures on twistor and reflector spaces of paraquaternionic contact manifolds.
problem Geometric structures on paraquaternionic contact manifolds.
method Investigate fiber bundles (twistor and reflector spaces) over paraquaternionic contact manifolds.
result Intrinsic geometric structures on twistor and reflector spaces are always integrable.
Variational approach to basic manifold structures.
problem Understanding basic differential geometric structures.
method Variational description of geometric structures.
result Variational formulation of manifold structures.
Proves modular functors for SO(3) have integral Hodge structures.
problem Proving modular functors have integral Hodge structures.
method Based on homological models and geometric identification.
result Geometric construction of Hodge structures on SO(3) modular functors.