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 Schouten solitons on Kenmotsu manifolds, focusing on torse-forming vector fields.
Defines and classifies algebraic Schouten solitons in 3D Lorentzian Lie groups.
The paper proves inequalities and growth rates for Schouten solitons.
The paper proves rigidity of certain solitons with specific properties.
The paper solves gradient Schouten solitons on specific geometric structures.
Study of ends of complete gradient Schouten solitons, showing finitely many ends for shrinking and connected infinity for expanding ones.
Paper classifies Schouten-like metrics on 5D nilpotent Lie groups.
The study finds a lower bound for the diameter of gradient ρ-Einstein solitons.
New solitons defined for Sasaki-like almost contact complex Riemannian manifolds.
Defines and proves properties of weighted renormalized volume coefficients.
The main purpose of this paper is to investigate the Schouten-Weyl tensor on the three-dimensional Lie groups with left-invariant Lorenzian metrics. The left-invariant Lorentzian metrics on the three-dimensional Lie groups with squared length zero Schouten-Weyl tensor are studied. Moreover, the three-dimensional metric…
New metrics for information geometry and machine learning from Lie groups.
Develops Schouten-Nijenhuis bracket on infinite-dimensional manifolds.
We show that an eternal solution to a complete, locally conformally flat Yamabe flow, , with uniformly bounded scalar curvature and positive Ricci curvature at , where the scalar curvature assumes its maximum is a gradient steady soliton. As an application of that, we study t…
On a manifold with boundary, we deform the metric conformally. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior, provided that there exists a subsolution.
The study explores Lie superalgebras constructed from Lie algebras using Schouten-like brackets.
New proof confirms noncompact locally conformally flat manifolds are compact.
The paper derives Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
This paper compiles formulas involving differential operators and interior products.
Solves modified Schouten tensor problems in conformal metric classes.
We show how to extend the construction of Tulczyjew triples to Lie algebroids via graded manifolds. We also provide a generalisation of triangular Lie bialgebroids as higher Poisson and Schouten structures on Lie algebroids.
Generalized Schouten, Froelicher-Nijenhuis and Froelicher-Richardson brackets are defined for an arbitrary Lie algebroid. Tangent and cotangent lifts of Lie algebroids are introduced and discussed and the behaviour of the related graded Lie brackets under these lifts is studied. In the case of the canonical Lie algebro…
We show that -algebroids, understood in terms of Q-manifolds can be described in terms of certain higher Schouten and Poisson structures on graded (super)manifolds. This generalises known constructions for Lie (super)algebras and Lie algebroids.
We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.
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…
In the presented paper left-invariant pseudo-Riemannian metrics on four-dimensional Lie groups with zero Schouten-Weyl tensor are investigated. The complete classification of these metric Lie groups is obtained in terms of the structure constants of corresponding Lie algebras.
New connections defined for a specific geometric structure.
In this paper we study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Schouten tensor on compact Riemannian manifolds with boundary. We prove its solvability and the compactness of the solution set, provided the Ricci tensor is non-negative definite.
Quantizes the relationship between Koszul and Schouten brackets in Poisson geometry.
The paper calculates curvature limits and Gauss-Bonnet theorems in the Heisenberg group.
This short note contains an explicit proof of the Jacobi identity for variational Schouten bracket in -graded commutative setup. For the reasoning to be rigorous, it refers to the product bundle geometry of iterated variations (see arXiv:1312.1262 [math-ph]); no ad hoc regularizations occur anywhere in this theory…
The Schouten bracket (or antibracket) plays a central role in the Poisson formalism and the Batalin-Vilkovisky quantization of gauge systems. There are several (in)equivalent ways to realize this concept on jet spaces. In this paper, we compare the definitions, examining in what ways they agree or disagree and how they…
Let N be a symmetric space of dimension n > 5 whose de Rham decomposition contains no factors of constant curvature and let W be the Weyl tensor of N at some point. We prove that a Riemannian manifold whose Weyl tensor at every point is a positive multiple of W is conformally equivalent to N (the case N = R^n is the We…
Defines conditions for unique conformal metrics on manifolds with specific curvature properties.
Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we …
Paper traces origins of graded Lie brackets theory.
The paper explores metrics on Lie groups and their connections to dual quaternions.
Study on existence of metrics in conformal geometry with constraints on Schouten tensor.
There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic clas…
Solves curvature problems on manifolds with negative curvature.
The behavior under conformal change of the renormalized volume coefficients associated to a pseudo-Riemannian metric is investigated. It is shown that they define second order fully nonlinear operators in the conformal factor whose algebraic structure is elucidated via the introduction of "extended obstruction tensors"…
Paper introduces p-Laplace equations for curvature in conformal geometry.
Researchers solve metric curvature equations on manifolds with boundary.
The note is about some nonlinear curvature conditions which arise naturally in conformal geometry.
The paper constructs compatible Poisson brackets on gl(N).
We prove a Darboux theorem for formal deformations of Hamiltonian operators of hydrodynamic type (Dubrovin-Novikov). Not all deformations are equivalent to the original operator: there is a moduli 2-stack of normal forms. The paper utilizes three main concepts: 1) dg Lie algebras concentrated in degrees [-1,\infty) suc…
We generalize the Schouten calculus of multivector fields to commutative Lie Rinehart pairs and define a non negatively graded Lie oo-algebra on their exterior power.
The geometric approach [1312.1262] to iterated variations of local functionals -- e.g., of the (master-)action functional -- resulted in an extension of the deformation quantisation technique to the set-up of Poisson models of field theory [IHES/M/15/13]. It also allowed of a rigorous proof ([1312.1262],[1210.0726]) fo…