Results 1 to 10 of about 44,281 (143)
Another approach to the fundamental theorem of Riemannian geometry in
Journal de Mathématiques Pures et Appliquées, 2006 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
Philippe G. Ciarlet +4 more
semanticscholar +7 more sources
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
doaj +2 more sources
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
doaj +4 more sources
Warped Riemannian metrics for location-scale models [PDF]
Geometric Structures of Information, 2017 The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry.
A Terras +42 more
core +2 more sources
Every conformal class contains a metric of bounded geometry [PDF]
, 2015 We show that on every manifold, every conformal class of semi-Riemannian metrics contains a metric $g$ such that each $k$-th-order covariant derivative of the Riemann tensor of $g$ has bounded absolute value $a_k$.
Müller, Olaf, Nardmann, Marc
core +3 more sources
Riemannian curvature measures [PDF]
Geometric and Functional Analysis, 2017 A famous theorem of Weyl states that if M is a compact submanifold of euclidean space, then the volumes of small tubes about M are given by a polynomial in the radius r, with coefficients that are expressible as integrals of certain scalar invariants of ...
Joseph H. G. Fu, Thomas Wannerer
semanticscholar +2 more sources
Nonlinear elasticity complex and a finite element diagram chase [PDF]
arXiv.org, 2023 In this paper, we present a nonlinear version of the linear elasticity (Calabi, Kr\"oner, Riemannian deformation) complex which encodes isometric embedding, metric, curvature and the Bianchi identity. We reformulate the rigidity theorem and a fundamental
Kaibo Hu
semanticscholar +1 more source
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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Generalized cylinders in semi-Riemannian and spin geometry [PDF]
, 2003 .We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings ...
Christian Bär +2 more
semanticscholar +1 more source
Unimodular measures on the space of all Riemannian manifolds [PDF]
, 2020 We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups of Lie groups.
Abert, Miklos, Biringer, Ian
core +2 more sources