Results 1 to 10 of about 43,102 (116)
On the Non Metrizability of Berwald Finsler Spacetimes [PDF]
Universe, 2020 We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern–Rund ...
Andrea Fuster +3 more
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Another approach to the fundamental theorem of Riemannian geometry in
Journal de Mathématiques Pures et Appliquées, 2007 AbstractIn 1992, C. Vallée showed that the metric tensor field C=∇ΘT∇Θ associated with a smooth enough immersion Θ:Ω→R3 defined over an open set Ω⊂R3 necessarily satisfies the compatibility relationCURLΛ+COFΛ=0in Ω, where the matrix field Λ is defined in terms of the field U=C1/2 byΛ=1detU{U(CURLU)TU−12(tr[U(CURLU)T])U}.The main objective of this paper
Ciarlet, Philippe +4 more
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Riemannian Geometry and the Fundamental Theorem of Algebra
, 2011 If a (non-constant) polynomial has no zero, then a certain Riemannian metric is constructed on the two dimensional sphere. Several geometric arguments are then shown to contradict this fact.
Almira, J. M., Romero, A.
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The Reciprocal of the Fundamental Theorem of Riemannian Geometry
, 2009 The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions. Even though Ricardo's formula can mathematically give the full answer, it is argued that the solution should be taken only up to a constant conformal factor ...
Héctor H. Calderón
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Rotation fields and the fundamental theorem of Riemannian geometry in
Comptes Rendus. Mathématique, 2006 Let Ω be a simply-connected open subset of R^3. We show that, if a smooth enough field U of symmetric and positive-definite matrices of order three satisfies the compatibility relation (due to C. Vallee) CURL Λ+COF Λ=0 in Ω, where the matrix field Λ is defined in terms of the field U by Λ=(1/detU){U(CURL U)^T U−(1/2)(tr[U(CURL U)T])U ...
Ciarlet, Philippe G. +4 more
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Riemannian Structures on
Mathematics, 2020 Very loosely, Z2n-manifolds are ‘manifolds’ with Z2n-graded coordinates and their sign rule is determined by the scalar product of their Z2n-degrees. A little more carefully, such objects can be understood within a sheaf-theoretical framework, just as ...
Andrew James Bruce, Janusz Grabowski
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Natural SU(2)-structures on tangent sphere bundles [PDF]
, 2020 We define and study natural $\mathrm{SU}(2)$-structures, in the sense of Conti-Salamon, on the total space $\cal S$ of the tangent sphere bundle of any given oriented Riemannian 3-manifold $M$.
Albuquerque, R.
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New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology [PDF]
, 2006 We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative
A. Manning +12 more
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Some Curvature Problems in Semi-Riemannian Geometry [PDF]
, 2010 In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of ...
AN Bernal +20 more
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Fill Radius and the Fundamental Group [PDF]
, 2009 In this note we relate the geometric notion of fill radius with the fundamental group of the manifold. We prove: ''Suppose that a closed Riemannian manifold M satisfies the property that its universal cover has bounded fill radius.
Ramachandran, Mohan, Wolfson, Jon
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