| 《几何分析手册(第3卷)》：The launch of this Advanced Lectures in Mathematics series is aimed at keepingmathematicians informed of the latest developments in mathematics, as well asto aid in the learning of new mathematical topics by students all over the world.Each volume consists of either an expository monograph or a collection of signifi-cant introductions to important topics. This series emphasizes the history andsources of motivation for the topics under discussion, and also gives an overviewof the current status of research in each particular field. These volumes are thefirst source to which people will turn in order to learn new subjects and to dis-cover the latest results of many cutting-edge fields in mathematics. |
| a survey of einstein metrics on 4-manifolds michael t. anderson 1 introduction 2 brief review: 4-manifolds, complex surfaces and einstein metrics 3 constructions of einstein metrics i 4 obstructions to einstein metrics 5 moduli spaces i 6 moduii spaces ii 7 constructions of einstein metrics ii 8 concluding remarks references sphere theorems in geometry simon brendle, richard schoen 1 the topological sphere theorem 2 manifolds with positive isotropic curvature 3 the differentiable sphere theorem 4 new invariant curvature conditions for the ricci flow 5 rigidity results and the classification of weakly 1/4-pinched manifolds 6 hamilton's differential harnack inequality for the ricci flow 7 compactness of pointwise pinched manifolds references curvature flows and cmc hypersurfaces claus gerhardt 1 introduction 2 notations and preliminary results 3 evolution equations for some geometric quantities. 4 essential parabolic flow equations 5 existence results 6 curvature flows in riemannian manifolds 7 foliation of a spacetime by cmc hypersurfaces 8 the inverse mean curvature flow in lorentzian spaces references geometric structures on riemannian manifolds naichung conan leung 1 introduction 2 topology of manifolds 2.1 cohomology and geometry of differential forms 2.2 hodge theorem 2.3 witten-morse theory 2.4 vector bundles and gauge theory 3 riemannian geometry 3.1 torsion and levi-civita connections 3.2 classification of riemannian holonomy groups 3.3 riemannian curvature tensors 3.4 flat tori 3.5 einstein metrics 3.6 minimal submanifolds 3.7 harmonic maps 4 oriented four manifolds 4.1 gauge theory in dimension four 4.2 riemannian geometry in dimension four 5 kaihler geometry 5.1 kahler geometry -- complex aspects 5.2 kahler geometry -- riemannian aspects 5.3 kahler geometry -- symplectic aspects 5.4 gromov-witten theory 6 calabi-yau geometry 6.1 calabi-yau manifolds 6.2 special lagrangian geometry 6.3 mirror symmetry 6.4 k3 surfaces 7 calabi-yau 3-folds 7.1 moduli of cy threefolds 7.2 curves and surfaces in calabi-yau threefolds 7.3 donaldson-thomas bundles over calabi-yau threefolds. 7.4 special lagrangian submanifolds in cy3 7.5 mirror symmetry for calabi-yau threefolds 8 g2-geometry 8.1 g2-manifolds 8.2 moduli of g2-manifolds 8.3 (co-)associative geometry 8.4 g2-donaldson-thomas bundles 8.5 g2-dualities, trialities and m-theory 9 geometry of vector cross products 9.1 vcp manifolds 9.2 instantons and branes 9.3 symplectic geometry on higher dimensional knot …… symplectic calabi-yau surfaces lectures on stability and constant scalar curvature analytic aspect of hamilton's ricci flow |
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