Tangent bundle
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Differential Systems Associated with Simple Graded Lie Algebras Open
This is a survey paper on differential systems associated with simple graded Lie algebras.By a differential system (M, D), we mean a pfaffian system D ( or a distribution in Chevalley's sense) on a manifold M, that is, D is a subbundle of …
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Finsler gravity action from variational completion Open
In the attempts to apply Finsler geometry to construct an extension of\ngeneral relativity, the question about a suitable generalization of the\nEinstein equations is still under debate. Since Finsler geometry is based on a\nscalar functio…
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Spectral convergence of the connection Laplacian from random samples Open
Journal Article Spectral convergence of the connection Laplacian from random samples Get access Amit Singer, Amit Singer Search for other works by this author on: Oxford Academic Google Scholar Hau-Tieng Wu Hau-Tieng Wu *Corresponding auth…
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$\mathcal{VB}$-groupoids and representation theory of Lie groupoids Open
A VB-groupoid is a Lie groupoid equipped with a compatible linear structure.\nIn this paper, we describe a correspondence, up to isomorphism, between\nVB-groupoids and 2-term representations up to homotopy of Lie groupoids. Under\nthis cor…
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Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes Open
We discuss the geodesic motion of both massive test particles, following timelike geodesics, and light, following null geodesics, on Finsler spacetimes with cosmological symmetry. Using adapted coordinates on the tangent bundle of the spac…
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Berwald spacetimes and very special relativity Open
In this work we study Berwald spacetimes and their vacuum dynamics, where the\nlatter are based on a Finsler generalization of the Einstein's equations\nderived from an action on the unit tangent bundle. In particular, we consider a\nspeci…
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Weyl connections and their role in holography Open
It is a well-known property of holographic theories that diffeomorphism invariance in the bulk space-time implies Weyl invariance of the dual holographic field theory in the sense that the field theory couples to a conformal class of backg…
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Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells Open
Chern-Schwartz-MacPherson (CSM) classes generalize to singular and/or noncompact varieties the classical total homology Chern class of the tangent bundle of a smooth compact complex manifold. The theory of CSM classes has been extended to …
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Relativistic kinetic gases as direct sources of gravity Open
We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas. The properties of the, colliding or non-colliding, particles are encoded into a so called one-particle distribution function, which…
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Invariant distributions and X-ray transform for Anosov flows Open
For Anosov flows preserving a smooth measure on a closed manifold\n$\\mathcal{M}$, we define a natural self-adjoint operator $\\Pi$ which maps into\nthe space of invariant distributions in $\\cap_{u0} H^{s}(\\mathcal{M})$. We\ndescribe rel…
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Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds Open
We give a systematic derivation of the local expressions of the NS H-flux, geometric F- as well as non-geometric Q- and R-fluxes in terms of bivector beta- and two-form B-potentials including vielbeins. They are obtained using a supergeome…
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Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle Open
We study field equations for a weak anisotropic model on the tangent Lorentz\nbundle $TM$ of a spacetime manifold. A geometrical extension of General\nRelativity (GR) is considered by introducing the concept of local anisotropy,\ni.e. a di…
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Complex Functional Maps: A Conformal Link Between Tangent Bundles Open
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness . More specifically, we…
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Examples of Fano manifolds with non‐pseudoeffective tangent bundle Open
Let $X$ be a Fano manifold. While the properties of the anticanonical divisor\n$-K_X$ and its multiples have been studied by many authors, the positivity of\nthe tangent bundle $T_X$ is much more elusive. We give a complete\ncharacterisati…
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Some notes on the tangent bundle with a Ricci quarter-symmetric metric connection Open
Let $ (M, g) $ be an $ n $-dimensional (pseudo-)Riemannian manifold and $ TM $ be its tangent bundle $ TM $ equipped with the complete lift metric $ ^{C}g $. First, we define a Ricci quarter-symmetric metric connection $ \overline{\nabla }…
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Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle Open
The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connect…
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Connecting Information Geometry and Geometric Mechanics Open
The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold Q × Q . We aim to investigate the relationship between thes…
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Codimension One Holomorphic Distributions on the Projective Three-space Open
We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree…
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Heterotic backgrounds via generalised geometry: moment maps and moduli Open
We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an SU(3) × Spin(6 + n) structure within O(6, 6 + n) x $\\ma…
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Computing distances and geodesics between manifold-valued curves in the SRV framework Open
This paper focuses on the study of open curves in a Riemannian manifold M, and proposes a reparametrization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. to def…
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TANGENT BUNDLE ENDOWED WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION ON AN ALMOST HERMITIAN MANIFOLD Open
In this paper, we have studied the tangent bundle endowed with quarter-symmetric non-metric connection obtained by vertical and complete lifts of a quarter-symmetric non-metric connection on the base manifold and, also, proposed the study …
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Cobordism invariants of the moduli space of stable pairs Open
For a quasi-projective scheme $M$ which carries a perfect obstruction theory, we construct the virtual cobordism class of $M$ which is the universal virtual fundamental class. If $M$ is projective, then we prove that the corresponding Cher…
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Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection Open
The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, (LPS)n) to its tangent bundle TM associated with a Riemannian connection DC …
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Geometry and stability of tautological bundles on Hilbert schemes of points Open
We explore the geometry and establish the slope-stability of tautological vector bundles on Hilbert schemes of points on smooth surfaces. By establishing stability in general, we complete a series of results of Schlickewei and Wandel, who …
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Dynamically consistent Jacobian inverse for non-holonomic robotic systems Open
This paper presents an extension of the concept of dynamically consistent Jacobian inverse from robotic manipulators (holonomic systems) to non-holonomic robotic systems, like mobile robots. This new inverse is derived within the framework…
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Jacobi Stability Analysis of Scalar Field Models with Minimal Coupling to Gravity in a Cosmological Background Open
We study the stability of the cosmological scalar field models by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In this approach, we describe the time evolution of the scalar field cosmologies in geometric …
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Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles Open
Presented herein are a class of methodologies for conducting constrained motion analysis of rigid bodies within the Udwadia-Kalaba (U-K) formulation. The U-K formulation, primarily devised for systems of particles, is advanced to rigid bod…
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Geometry of Mus-Sasaki metric Open
In this paper, we introduce the Mus-Sasaki metric on the tangent bundle T M as a new natural metric non-rigid on T M . First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar…
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Tangent Bundles of P-Sasakian Manifolds Endowed with a Quarter-Symmetric Metric Connection Open
The purpose of this study is to evaluate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection on the tangent bundle TM. Certain results on a semisymmetric P-Sasakian man…
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Coordinate free nonlinear incremental discrete mechanics Open
In this paper we extend the Kinematic Structural Stability (KISS) issues obtained in the punctual linear case to a full non linear framework. Kinematic Structural Stability (KISS) refers to the stability of conservative or non‐conservative…