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.
Study on invariant structures on 7D nilpotent Lie groups, focusing on Sasaki and K-contact.
A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding which Lie groups admit a left invariant contact structure (contact Lie groups), is t…
Prove an isoperimetric inequality for compact bodies in 3D contact non-unimodular Lie groups.
The paper classifies structures on specific Lie groups.
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and derive some obstruction results to the existence of left invariant contact structu…
We prove that a K-contact Lie group of dimension five or greater is the central extension of a symplectic Lie group by complexifying the Lie algebra and applying a result from complex contact geometry, namely, that, if the adjoint action of the complex Reeb vector field on a complex contact Lie algebra is diagonalizabl…
Study proves all left-invariant contact structures on 3D Lie groups are tight.
This paper investigates the geometry of compact contact manifolds that are uniformized by contact Lie groups, i.e., compact manifolds that are the quotient of some Lie group G with a left invariant contact structure and a uniform lattice subgroup. We re-examine Alexander's criteria for existence of lattices on solvable…
The paper finds a contact form on SL(2p) for p > 1.
Reduces equations for contact mechanical systems on Lie groups by exploiting symmetries.
Classifies semisimple symmetric contact spaces under Lie groups.
The object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the studied manifolds and the explicit matrix representation of Lie groups. Some kno…
Classifies 3D contact structures using Cartan connections.
Finite automorphisms group for certain CR manifolds.
We study left invariant contact forms and left invariant symplectic forms on Lie groups. We give the classification of all symplectic structures on nilpotent Lie algebras up the dimension 6.
Study on curvatures of surfaces in specific Lie groups.
We construct explicit left invariant quaternionic contact structures on Lie groups with zero and non-zero torsion, and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of quaternionic contact manifolds not locally quaternionic contact conformal to the quaternionic sphere. W…
The paper classifies para-Kähler structures on Lie groups.
We answer in the affirmative a question posed by Ivanov and Vassilev on the existence of a seven dimensional quaternionic contact manifold with closed fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an approach to the classification of seven dimensional solvable Lie groups having an integra…
Study contact partial order on non-compact manifolds.
We are interested in the class, in the Elie Cartan sense, of left invariant forms on a Lie group. We construct the class of Lie algebras provided with a contact form and classify the frobeniusian Lie algebras up to a contraction. We also study forms which are invariant by a subgroup. We show that the simple group SL(2n…
Jet spaces on Carnot groups have a canonical Lie group structure.
Develops k-contact geometry theory for field theories.
Almost contact manifolds with B-metric are considered. There are studied three natural connections (i.e. linear connections preserving the structure tensors) determined by conditions for their torsions. These connections are investigated on a family of Lie groups considered as 5-dimensional almost contact B-metric mani…
Smooth contact mappings in a flat (2,3,5)-distribution are shown to be smoother.
Almost contact B-metric manifolds of dimension 3 are constructed by a two-parametric family of Lie groups. The class of these manifolds in a known classification of almost contact B-metric manifolds is determined as the direct sum of the main vertical classes. The type of the corresponding Lie algebras in the Bianchi c…
Criterion for lifting smooth contact maps between Carnot groups to central extensions.
The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes. An example is given as a support of obtained results.
Classifies contact seaweeds based on their algebraic properties.
In this paper we study contact structure on 2-step nilpotent, Heisenberg type Lie groups. We decompose this Lie groups to center and orthogonal complement, then investigate properties of both orthogonal Lie subgroups. Finally, we provide a connection between matchings in groups and field extensions and 2-step nilpotent…
Three-dimensional almost contact B-metric manifolds are constructed by a three-parametric family of Lie groups. It is established the class of the investigated manifolds which has an important geometrical interpretation. It is determined also the type of the constructed Lie algebras in the Bianchi classification. There…
Study finds specific Lie groups with Kenmotsu structures.
A connected Fano complex-contact manifold is isomorphic to the kaehlerian C-space of Boothby type with a natural complex-contact structure corresponding to a non-abelian simple complex Lie algebra if the contact line bundle is very ample. A. Beauville relaxed the provision to two assumptions that the contact line bundl…
New realizations prove all candidates are Ricci solitons.
The study examines weakly Einstein metrics on specific types of manifolds.
We characterize the rigidity of Carnot groups in the class of contact maps in terms of complex characteristics. Furthermore, we obtain a Liouville type theorem for Carnot groups which states that 1-quasiconformal maps form finite dimensional Lie groups.
We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact structures from a counterpart of generalized complex structures on odd-dimensiona…
Reduces LCS manifolds with symplectic actions, preserving conformal structure.
New insights into 5D Sasakian Lie algebras with trivial center.
Study on surface geometry in Lie groups with CR structures.
Study locally conformal symplectic manifolds on compact nilmanifolds.
We continue the study of linear families of contact forms on 3-manifolds begun in our paper `Contact geometry and complex surfaces'. The present paper introduces Teichmuller and moduli spaces for so-called taut contact circles. By constructing a developing map for taut contact circles, we show that these geometrically …
Yamabe solitons defined on specific Sasaki-like manifolds.
Study of abelian structures on odd-dimensional Lie algebras and their geometric properties.
In this paper we consider symplectic and contact Lie algebras. We define contactization and symplectization procedures and describe its main properties. We also give classification of such algebras in dimensions 3 and 4. The classification in dimension~4 is closely connected with normal forms of nondegenerate elliptic …
Classifies homogeneous Riemannian structures on 3D Lie groups.
Study compatible and associated metrics for contact-symplectic structures, showing geodesic integral curves and minimal leaf properties.
Study of marked contact Engel structures with geometric invariants.