The authors first in this paper define a semi-symmetric metric non-holonomic connection (called in briefly a semi-sub-Riemannian connection) on sub-Riemannian manifolds, and study the relations between sub-Riemannian connections and semi-sub-Riemannian connections. An invariant under a connection transformation $\nabla…
On-device research index
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.
169,341 papers · 148 categories
Trend · papers per month
48 results for “sub-Riemannian connection”
Study sub-Riemannian geometry on parallelizable distributions.
problem Investigate the geometry of sub-Riemannian structures on non-integrable parallelizable distributions.
method Construct and analyze two linear connections: Weitzenböck and sub-Riemannian.
result Two concrete examples (S^3 and S^7) illustrate the application of sub-Riemannian geometry.
The authors define a SNS (semi-nearly-sub)-Riemannian connection on nearly sub-Riemannian manifolds and study the geometric properties of such a connection, and obtain the natures of horizontal curvature tensors between horizontal sub-Riemannian connection and SNS-Riemannian connection. The authors further investigate …
A new connection defined in sub-Riemannian geometry.
problem Defining a canonical connection in sub-Riemannian contact geometry.
method Inspired by Levi-Civita connection, constructs an affine connection.
result Compares with Tanaka-Webster connection in 3D.
Introduces canonical connections for sub-Riemannian manifolds with constant symbol.
problem Equivalence problem in sub-Riemannian geometry.
method Introduces canonical grading and compatible affine connection.
result Completely computed structures for contact manifolds of constant symbol.
We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a contact manifold of dimension more than three is noncharacteristic or with isola…
Constructs stochastic processes on sub-Riemannian manifolds using Cartan connections.
problem Developing stochastic processes on sub-Riemannian manifolds.
method Introduces stochastic development using Cartan connections, derives generator, and provides conditions for existence.
result Derives a general expression for the generator of the stochastic process and provides conditions for the existence of a Cartan connection.
The paper develops a non-transitive Cartan connection for sub-Riemannian manifolds.
problem Analyzing sub-Riemannian structures and their symmetries.
method Using Lie groupoids and non-transitive Cartan connections.
result A non-transitive Cartan connection is constructed for sub-Riemannian manifolds.
New normalization condition for sub-Riemannian connections.
problem Normalizing connections on sub-Riemannian manifolds.
method Formulated in terms of Cartan connections, depends on curvature's first degree of homogeneity.
result A compatible partial affine connection can be uniquely extended to a full affine connection and a grading of the tangent bundle.
The paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.
problem Exploring new connections and conditions for specific types of manifolds.
method Defining a skew-symmetric connection and studying its properties on sub-Riemannian manifolds, and examining conditions for almost quasi-Sasakian manifolds to be Einstein.
result Sufficient conditions are found for an almost quasi-Sasakian manifold to be an Einstein manifold.
We solve the local equivalence problem for sub-Riemannian structures on (2n + 1)-dimensional manifolds. We show that two sub-Riemannian structures are locally equivalent if and only if? their corresponding canonical linear connections are equivalent. When n = 1, these connections coincide with the generalized Tanaka-We…
New method for curvature computation in sub-Riemannian geometry.
problem Computing curvature in sub-Riemannian manifolds.
method Using compatible affine connections and induced tensors.
result Universal Bonnet-Myers theorem for sub-Riemannian geometry.
The Prytz connectionsmath.DG
Mathematical analysis of Prytz planimeter using sub-Riemannian geometry.
problem Historical use of Prytz planimeter to approximate areas.
method Sub-Riemannian geometry and connections/horizontal lifts.
result Mathematical description and analysis of Prytz planimeter.
Maximal isometries define canonical connections in sub-Riemannian spaces.
problem Characterizing sub-Riemannian spaces with maximal isometry groups.
method Study of sub-Riemannian spaces with maximal isometry groups and canonical connections.
result Canonical connections generalize Levi-Civita connections and have more invariants.
We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties of this connection to justify our choice and show that this connection is unique in having these properties.
Study random walks on sub-Riemannian manifolds using retractions.
problem Modeling random walks on sub-Riemannian manifolds.
method Use retractions to approximate normal geodesics and study convergence to Brownian motion.
result Convergence of geodesic random walks defined with different connections.
Constant curvature models in sub-Riemannian geometry are explored.
problem Understanding constant curvature models in sub-Riemannian geometry.
method Cohomological description of principal invariants for parabolic geometries.
result Constant curvature models are discussed for specific sub-Riemannian geometries.
Variations of the sub-Riemannian distance on Sasakian manifolds with applications to couplingmath.DG
Maps on Sasakian manifolds limit to sub-Riemannian distance bounds.
problem Understanding sub-Riemannian distances on Sasakian manifolds.
method Parallel and mirror maps along geodesics of a taming Riemannian metric.
result Limits of transport maps outside sub-Riemannian cut-locus provide bounds on sub-Riemannian distance.
In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [Zelenko-Li]. We show why this connection is naturally nonlinear, and…
In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of sub-Riemannian metrics on totally geodesic Riemannian submersions…
Holonomy groups of K-contact sub-Riemannian manifolds are isomorphic.
problem Holonomy groups of K-contact sub-Riemannian manifolds.
method Proved isomorphism of holonomy groups under specific conditions.
result Holonomy groups of K-contact sub-Riemannian manifolds are isomorphic.
New equations for geodesics in sub-Riemannian geometry.
problem Finding equations for normal geodesics in sub-Riemannian geometry.
method Developed a new system of equations using a partial connection.
result The new equations split into horizontal and complementary parts.
We study sub-Riemannian and sub-Lorentzian geometry on the Lie group $\SU(1,1)$ and on its universal cover $\CSU(1,1)$. In the sub-Riemannian case we find the distance function and completely describe sub-Riemannian geodesics on both $\SU(1,1)$ and $\CSU(1,1)$, connecting two fixed points. In particular, we prove that …
Study holonomy in pseudo-Hermitian geometry structures.
problem Holonomy classification in pseudo-Hermitian geometry.
method Analyzes sub-Riemannian structures, torsion, and holonomy algebras.
result Holonomy groups of Schouten and adapted connections are related under certain conditions.
Sub-Riemannian geometry connects bike paths to mathematical curves.
problem Understanding bike paths and their mathematical properties.
method Relating sub-Riemannian geometry to bicycle motion and curve shapes.
result Geodesics in sub-Riemannian geometry correspond to specific bike paths.
Notes on sub-Riemannian geometry equivalence problem.
problem Isometric sub-Riemannian manifolds equivalence.
method Introduction to connections, frame bundles, and sub-Riemannian geometry; description of canonical grading and connection.
result Minimal set of isometries for Engel (2,3,4)-manifolds.
Essential self-adjointness proven for sub-Laplacians on sub-Riemannian manifolds.
problem Proving essential self-adjointness for sub-Laplacians on sub-Riemannian manifolds.
method General essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures.
result Intrinsic sub-Laplacian is essentially self-adjoint on equiregular connected components of a sub-Riemannian manifold under mild regularity assumptions.
Study of sub-Riemannian problem on specific Lie groups, revealing symmetries and bounds.
problem Sub-Riemannian problem on solvable, non-nilpotent Lie groups.
method Qualitative phase-space analysis of Hamiltonian system, focusing on vertical component.
result Explicit upper bound for cut time in terms of pendulum period.
New exponential map for Lie groups connects to sub-Riemannian geometry.
problem Developing a new exponential map for Lie groups.
method Introducing a new exponential map related to sub-Riemannian geometry.
result New exponential map connects to sub-Riemannian geometry.
The paper calculates curvature limits and Gauss-Bonnet theorems in the Heisenberg group.
problem Computing curvature limits and Gauss-Bonnet theorems in the Heisenberg group.
method Sub-Riemannian limits of Gaussian curvature, Schouten-Van Kampen affine connections, and adapted connections.
result Gauss-Bonnet theorems associated with Schouten-Van Kampen affine connections in the Heisenberg group.
New model explains visual illusions using sub-Riemannian geometry.
problem Mathematical modeling of Poggendorff-type visual illusions.
method Cortical-inspired sub-Riemannian model with sub-Laplacian evolution.
result Sub-Riemannian kernel enhances visual misperceptions and biases.
We find a different approach to define convex functions in the sub-Riemannian setting. A function on a sub-Riemannian manifold is nonholonomically geodesic convex if its restriction to any nonholonomic (straightest) geodesic is convex. In the case of Carnot groups, this definition coincides with that by Danniell-Garofa…
We give a generalized curvature-dimension inequality connecting the geometry of sub-Riemannian manifolds with the properties of its sub-Laplacian. This inequality is valid on a large class of sub-Riemannian manifolds obtained from Riemannian foliations. We give a geometric interpretation of the invariants involved in t…
Model explains optical illusions using geometric sub-Riemannian geodesics.
problem Understanding and explaining geometrical optical illusions.
method Neuro-mathematical model based on sub-Riemannian geodesics in the Roto-Translation Group.
result Illusory contours are described as geodesics in a new metric.
We give the complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. This classifications recovers other known classification results in the literature, in particular the one obtained in [Falbel-Gorodski, 1996] in terms of curvatu…
The paper proves Weyl projective rigidity for sub-Riemannian metrics and shows genericity of such metrics.
problem Investigating the Weyl projective rigidity of sub-Riemannian metrics.
method Analytic and smooth category proofs for specific distributions with minimal order complex abnormal extremals.
result Genericity of Weyl projectively rigid sub-Riemannian metrics and distributions.
A new image completion method inspired by brain cells.
problem Image restoration from corrupted data.
method Biologically-inspired sub-Riemannian model with frequency and phase.
result Completion of two-dimensional images using cortical cell responses.
We study a new class of rank two sub-Riemannian manifolds encompassing Riemannian manifolds, CR manifolds with vanishing Webster-Tanaka torsion, orthonormal bundles over Riemannian manifolds, and graded nilpotent Lie groups of step two. These manifolds admit a canonical horizontal connection and a canonical sub-Laplaci…
Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure is provided by the 3-D Heisenberg group. Sub-Riemannian Geometry enjoys major differences from the Riemannian being a generalisation of the la…
Two stochastic representations help prove infinite lifetime and bound gradients on sub-Riemannian manifolds.
problem Proving infinite lifetime and finding gradient bounds on sub-Riemannian manifolds.
method Using stochastic representations of heat semigroups and interplay between sub-Riemannian geometry and connections.
result Explicit pointwise bounds for horizontal gradients on Carnot groups.
We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In particular, some necessary and sufficient conditions for the existence of abnorm…
The article proves integral formulas for foliated sub-Riemannian manifolds.
problem Integral formulas for foliated sub-Riemannian manifolds.
method Proved a series of integral formulae involving mean curvatures, Newton transformations, and curvature tensor.
result Generalized known integral formulas for codimension-one foliations.
We show that the group of smooth isometries of a complemented sub-Riemannian manifold form a Lie group and establish dimension estimates based on the torsion of the canonical connection. We explore the interaction of curvature and the structure of isometries and Killing fields and derive a Bochner formula for Killing f…
New theorems show non-embeddability of certain Lie groups and sub-Riemannian manifolds.
problem Non-embeddability of Lie groups and sub-Riemannian manifolds in specific metric spaces.
method Proving non-existence of quasi-isometric embeddings and biLipschitz embeddings into certain metric measure spaces.
result Connected nonabelian nilpotent Lie groups and sub-Riemannian manifolds cannot be embedded into specified metric spaces.
The article derives integral formulas for foliated sub-Riemannian manifolds.
problem Integrating geometric concepts in Riemannian manifolds with foliations.
method Deriving integral formulas involving shape operators and curvature tensor.
result Generalizes results for foliated Riemannian manifolds and includes arbitrary functions.
In this paper we study geodesics of left-invariant sub-Riemannian metrics on SO(3) and almost-Riemannian metrics on . These structures are connected with each other, and it is possible to use information about one of them to obtain results about another one. We give an explicit parameterization of sub-Riemannian g…
Holomorphic functions on certain manifolds are isometric to Lie groups.
problem Characterizing holomorphic functions on specific Hermitian manifolds.
method Gradient estimate for holomorphic functions, sub-Riemannian geometry.
result Universal cover of complete Hermitian manifolds with flat Chern connection is holomorphically isometric to a complex Lie group.
This paper analyses the parabolic geometries generated by a free -distribution in the tangent space of a manifold. It shows that certain holonomy reductions of the associated normal Tractor connections, imply preferred connections with special properties, along with Riemannian or sub-Riemannian structures on the man…