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Titlebook: Aspects of Differential Geometry III; Esteban Calviño-Louzao,Eduardo García-Río,JeongHye Book 2017 Springer Nature Switzerland AG 2017

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期刊全称Aspects of Differential Geometry III
影响因子2023Esteban Calviño-Louzao,Eduardo García-Río,JeongHye
视频video
学科分类Synthesis Lectures on Mathematics & Statistics
图书封面Titlebook: Aspects of Differential Geometry III;  Esteban Calviño-Louzao,Eduardo García-Río,JeongHye Book 2017 Springer Nature Switzerland AG 2017
影响因子Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book III is aimed at the first-year graduate level but is certainly accessible to advanced undergraduates. It deals with invariance theory and discusses invariants both of Weyl and not of Weyl type; the Chern‒Gauss‒Bonnet formula is treated from this point of view. Homothety homogeneity, local homogeneity, stability theorems, and Walker geometry are discussed. Ricci solitons are presented in the contexts of Riemannian, Lorentzian, and affine geometry.
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Homothety Homogeneity and Local Homogeneity,f Lorentzian Walker manifolds. We determine which elements of the family are 0-curvature homogeneous, which are 1-curvature homogeneous, and which are 2-curvature homogeneous; for this family, 2-curvature homogeneity will in fact imply local homogeneity. A similar analysis of homothety curvature hom
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FM Global Reduced-Commodity Testing,er–Lagrange equations defined by Chern forms which generalize the corresponding Euler–Lagrange equations for the Pfaffian discussed previously. In Section 9.5, we give some examples of . (VSI) manifolds; these are pseudo-Riemannian manifolds all of whose scalar Weyl invariants vanish. We also develo
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,SN 1987A und unsere nächste Supernova,f Lorentzian Walker manifolds. We determine which elements of the family are 0-curvature homogeneous, which are 1-curvature homogeneous, and which are 2-curvature homogeneous; for this family, 2-curvature homogeneity will in fact imply local homogeneity. A similar analysis of homothety curvature hom
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Homothety Homogeneity and Local Homogeneity,omothety homogeneity. Let . be a homothety homogeneity manifold which has non-trivial homotethy character, i.e., which admits a diffeomorphism ∅ so ∅*g = λ.g for λ. ≠ 1. In Section 10.1, we show that if . is not VSI, then . is not homogeneous and present other foundational material. In Section 10.2,
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