Geometric structures associated with the Chern connection attached to a SODE [PDF]
Differential Geometry and its Applications, 2013 To each second-order ordinary differential equation $ $ on a smooth manifold $M$ a $G$-structure $P^ $ on $J^1(\mathbb{R},M)$ is associated and the Chern connection $\nabla ^ $ attached to $ $ is proved to be reducible to $P^ $; in fact, $P^ $ coincides generically with the holonomy bundle of $\nabla ^ $.
J. Muñoz Masqué, E. Rosado María
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Cubo, 2022 We investigate Monge-Amp\`ere type equations on almost Hermitian manifolds and show an \textit{a priori} $L^\infty$ estimate for a smooth solution of these equations.
Masaya Kawamura
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Groupoids in Sikorski’s spaces, connections and the Chern-Weil homomorphism [PDF]
Banach Center Publications, 2001 Krzysztof Lisiecki
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The Hodge Chern character of holomorphic connections as a map of simplicial presheaves [PDF]
Algebraic & Geometric Topology, 2022 We define a map of simplicial presheaves, the Chern character, that assigns to every sequence of composable non connection preserving isomorphisms of vector bundles with holomorphic connections an appropriate sequence of holomorphic forms. We apply this Chern character map to the Cech nerve of a good cover of a complex manifold and assemble the data by
Cheyne Glass +3 more
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On the Zakharov–Mikhailov action: $$4\hbox {d}$$ Chern–Simons origin and covariant Poisson algebra of the Lax connection [PDF]
Letters in Mathematical Physics, 2020 We derive the $$2\hbox {d}$$ 2 d Zakharov–Mikhailov action from $$4\hbox {d}$$ 4 d
V. Caudrelier +2 more
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Corrigendum to "Chern connection of a pseudo-Finsler metric as a family of affine connections" [PDF]
Publicationes Mathematicae Debrecen, 2014 In this note, we give the correct statements of [2,Proposition 3.3 and Theorem 3.4] and a formula of the Chern curvature in terms of the curvature tensor $R^V$ of the affine connection $\nabla^V$ and the Chern tensor $P$.
Miguel Ángel Javaloyes
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The Chern-Finsler connection and Finsler-Kähler manifolds [PDF]
Advanced Studies in Pure Mathematics, 2019 In this paper, we shall discuss the theory of connection in complex Finsler geometry, i.e., the Chern-Finsler connection $\nabla$ and its applications. In particular, we shall investigate (1) the ampleness of holomorphic vector bundles over a compact complex manifold which is based on the study due to [Ko1], (2) some special class of complex Finsler ...
Tadashi Aikou
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Chiral gravitational waves in Palatini-Chern-Simons gravity [PDF]
Physical Review D, 2022 We study the parity-breaking higher-curvature gravity theory of Chern-Simons (CS), using the Palatini formulation in which the metric and connection are taken to be independent fields.
Felipe Sulantay +2 more
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An inner product for 4D quantum gravity and the Chern–Simons–Kodama state [PDF]
Classical and quantum gravity, 2022 We demonstrate that reality conditions for the Ashtekar connection imply a non-trivial measure for the inner product of gravitational states in the polarization where the Ashtekar connection is diagonal, and we express the measure as the determinant of a
S. Alexander, G. Herczeg, L. Freidel
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General solutions in Chern-Simons gravity and T T ¯ $$ T\overline{T} $$ -deformations
Journal of High Energy Physics, 2021 We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection.
Eva Llabrés
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