About: Global differential geometry

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Attributs	Valeurs
type	Concept
rdfs:seeAlso	Geometries with differentiable structure Fiber spaces and bundles Differential topology Global analysis, analysis on manifolds
skos:inScheme	MSC 2010
broader concept	Differential geometry
narrower concept	Connections, general theory Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) Gerbes, differential characters: differential geometric aspects <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$ G$"><mml:mi>G</mml:mi></mml:math>-structures Foliations (differential geometric aspects) General geometric structures on manifolds (almost complex, almost product structures, etc.) Sub-Riemannian geometry Global Riemannian geometry, including pinching Methods of Riemannian geometry, including PDE methods; curvature restrictions Geodesics Global geometric and topological methods (Ã¡ la Gromov); differential geometric analysis on metric spaces Rigidity results Special Riemannian manifolds (Einstein, Sasakian, etc.) Hyper-KÃ¤hler and quaternionic KÃ¤hler geometry, ``special'' geometry Spin and Spin${}^c$ geometry Twistor methods Issues of holonomy Homogeneous manifolds Symmetric spaces Calibrations and calibrated geometries Global submanifolds Immersions (minimal, prescribed curvature, tight, etc.) Differential geometric aspects of harmonic maps Geometric evolution equations (mean curvature flow, Ricci flow, etc.) Global surface theory (convex surfaces Ã¡ la A. D. Aleksandrov) Lorentz manifolds, manifolds with indefinite metrics Hermitian and KÃ¤hlerian manifolds Other complex differential geometry Finsler spaces and generalizations (areal metrics) Integral geometry Direct methods (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$ G$"><mml:mi>G</mml:mi></mml:math>-spaces of Busemann, etc.) Geometric orders, order geometry Applications to physics None of the above, but in MSC2010 section 53Cxx
skos:prefLabel	Geometria differenziale globale Global differential geometry 整体微分几何(相关丛理论, 见55Rxx, 57Rxx)
skos:exactMatch	http://msc2010.org/resources/MSC/2000/53Cxx
skos:altLabel	Geometria differenziale globale [Vedi anche 51H25, 58-XX] {Per la teoria dei fibrati collegata, vedi 55Rxx, 57Rxx} 整体微分几何[参见51H25, 58-XX](相关丛理论, 见55Rxx, 57Rxx) Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]
http://msc2010.org...0/msc2010#seeAlso	Geometries with differentiable structure Global analysis, analysis on manifolds
http://msc2010.org...#seeConditionally	Fiber spaces and bundles Differential topology
http://msc2010.org...10/msc2010#seeFor	http://msc2010.org/resources/MSC/2010/53Cxx-to-55Rxx-seeFor http://msc2010.org/resources/MSC/2010/53Cxx-to-57Rxx-seeFor
skos:closeMatch	from MSC1991 value of: Global differential geometry, [See also 51H25, 58-XX; for related bundle theory, See 55Rxx, 57Rxx]
skos:notation	53Cxx
skos:note	See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx. See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx.
skos:relatedMatch	http://msc2010.org/resources/MSC/2010/fullDD21-516.36
skos:semanticRelation	Geometries with differentiable structure Fiber spaces and bundles Differential topology Global analysis, analysis on manifolds
is rdfs:seeAlso of	KÃ¤hler-Einstein manifolds Partial differential equations on manifolds Geometries with differentiable structure Global analysis, analysis on manifolds Spaces and manifolds of mappings (including nonlinear versions of 46Exx) Partial differential equations on manifolds; differential operators Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.)
is broader concept of	Connections, general theory Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) Gerbes, differential characters: differential geometric aspects <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$ G$"><mml:mi>G</mml:mi></mml:math>-structures Foliations (differential geometric aspects) General geometric structures on manifolds (almost complex, almost product structures, etc.) Sub-Riemannian geometry Global Riemannian geometry, including pinching Methods of Riemannian geometry, including PDE methods; curvature restrictions Geodesics Global geometric and topological methods (Ã¡ la Gromov); differential geometric analysis on metric spaces Rigidity results Special Riemannian manifolds (Einstein, Sasakian, etc.) Hyper-KÃ¤hler and quaternionic KÃ¤hler geometry, ``special'' geometry Spin and Spin${}^c$ geometry Twistor methods Issues of holonomy Homogeneous manifolds Symmetric spaces Calibrations and calibrated geometries Global submanifolds Immersions (minimal, prescribed curvature, tight, etc.) Differential geometric aspects of harmonic maps Geometric evolution equations (mean curvature flow, Ricci flow, etc.) Global surface theory (convex surfaces Ã¡ la A. D. Aleksandrov) Lorentz manifolds, manifolds with indefinite metrics Hermitian and KÃ¤hlerian manifolds Other complex differential geometry Finsler spaces and generalizations (areal metrics) Integral geometry

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