Search results for "Ricci flow"

showing 4 items of 4 documents

Born-Infeld gravity and its functional extensions

2014

We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the connection and an Einstein-like representation for the metric field equations of this family of theories. For particular cases we consider applications to the early-time cosmology and find that non-singular universes with a cosmic bounce are very generic and robust solutions.

High Energy Physics - TheoryPhysicsNuclear and High Energy PhysicsFOS: Physical sciencesClassical field theoryRicci flowGeneral Relativity and Quantum Cosmology (gr-qc)General Relativity and Quantum CosmologyClassical unified field theoriesTheoretical physicsEinstein tensorsymbols.namesakeHigh Energy Physics - Theory (hep-th)Born–Infeld modelsymbolsRicci decompositionf(R) gravityRicci curvaturePhysical Review D
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Weak Levi-Civita Connection for the Damped Metric on the Riemannian Path Space and Vanishing of Ricci Tensor in Adapted Differential Geometry

2001

Abstract We shall establish in the context of adapted differential geometry on the path space P m o ( M ) a Weitzenbock formula which generalizes that in (A. B. Cruzeiro and P. Malliavin, J. Funct. Anal . 177 (2000), 219–253), without hypothesis on the Ricci tensor. The renormalized Ricci tensor will be vanished. The connection introduced in (A. B. Cruzeiro and S. Fang, 1997, J. Funct. Anal. 143 , 400–414) will play a central role.

Weyl tensorRiemann curvature tensorCurvature of Riemannian manifoldsMathematical analysisRicci flowsymbols.namesakeLanczos tensorsymbolsRicci decompositionTensor densityRicci curvatureAnalysisMathematical physicsMathematicsJournal of Functional Analysis
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Ricci Tensors on Some Infinite Dimensional Lie Algebras

1999

Abstract The Ricci tensor has been computed in several infinite dimensional situations. In this work, we shall be interested in the case of the central extension of loop groups and in the asymptotic behaviour of the Ricci tensor on free loop groups as the Riemannian metric varies.

Weyl tensorPure mathematicsRiemann curvature tensorCurvature of Riemannian manifoldsMathematical analysisRicci flowEinstein tensorsymbols.namesakeLanczos tensorsymbolsRicci decompositionMathematics::Differential GeometryRicci curvatureAnalysisMathematicsJournal of Functional Analysis
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Ricci-flow based conformal mapping of the proximal femur to identify exercise loading effects.

2018

AbstractThe causal relationship between habitual loading and adaptive response in bone morphology is commonly explored by analysing the spatial distribution of mechanically relevant features. In this study, 3D distribution of features in the proximal femur of 91 female athletes (5 exercise loading groups representing habitual loading) is contrasted with 20 controls. A femur specific Ricci-flow based conformal mapping procedure was developed for establishing correspondence among the periosteal surfaces. The procedure leverages the invariance of the conformal mapping method to isometric shape differences to align surfaces in the 2D parametric domain, to produce dense correspondences across an…

Surface (mathematics)AdultModels Anatomicfyysinen rasitusluulcsh:Medicine030209 endocrinology & metabolismConformal mapIsometric exerciseStatistical parametric mappingbonebiomechanicsArticle030218 nuclear medicine & medical imagingdifferentiaaligeometria03 medical and health sciencesYoung Adult0302 clinical medicinereisiluuStatistical inferenceImage Processing Computer-AssistedHumansFemurFemurdifferential geometrylcsh:ScienceExerciseParametric statisticsMathematicsMultidisciplinarybusiness.industrylcsh:RRicci flowPattern recognition217 Medical engineeringBiomechanical PhenomenaAthletesphysical stressCase-Control Studieslcsh:QfemurFemalebiomekaniikkaArtificial intelligencebusinessAlgorithmsScientific reports
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