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LEVI–CIVITA CONNECTION ON ALMOST COMMUTATIVE ALGEBRAS
International Journal of Geometric Methods in Modern Physics, 2007Recently we introduced a new definition of metrics on almost commutative algebras. In this paper, we propose a coherent notion of compatible linear connection with respect to any almost commutative tensor and show that to every metric there corresponds a unique torsion-free compatible connection. This connection is called the Levi–Civita connection of
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Levi-Civita Connections on Degenerate Pseudo-Riemannian Manifolds
Journal of Mathematical Sciences, 2001The author studies smooth manifolds with degenerate symmetric bilinear form of constant signature on tangent spaces. He gives necessary and sufficient conditions for the existence of a Levi-Civita connection on such manifolds using cyclicity condition.
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Characterization of Levi-Civita and Newton–Cartan connections in dimension 2
Differential Geometry and its Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2018
On each Riemannian or pseudo-Riemannian manifold, there is a unique connection determined by the metric, called the Levi-Civita connection. After defining it, we investigate the exponential map, which conveniently encodes the collective behavior of geodesics and allows us to study the way they change as the initial point and initial velocity vary.
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On each Riemannian or pseudo-Riemannian manifold, there is a unique connection determined by the metric, called the Levi-Civita connection. After defining it, we investigate the exponential map, which conveniently encodes the collective behavior of geodesics and allows us to study the way they change as the initial point and initial velocity vary.
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4 Harmonic layer potentials associated with the Levi–Civita connection on UR domains
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2018We study metrizable projective structures near non-linearizable singularities of projective vector fields. We prove connected 3-dimensional Riemannian manifolds and closed connected pseudo-Riemannian manifolds admitting a projective vector field with a non-linearizable singularity are projectively flat.
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