Verlag: Morgan & Claypool Publishers, 2015
ISBN 10: 1627056629 ISBN 13: 9781627056625
Sprache: Englisch
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Verlag: Morgan & Claypool Publishers, 2015
ISBN 10: 1627057838 ISBN 13: 9781627057837
Sprache: Englisch
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Verlag: Springer International Publishing AG, CH, 2015
ISBN 10: 3031012801 ISBN 13: 9783031012808
Sprache: Englisch
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In den WarenkorbPaperback. Zustand: New. 1°. 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 II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology ofcompact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.
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In den WarenkorbHardback. Zustand: New. new copies no faults. Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces {which} are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2.
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Verlag: Springer, Berlin|Springer International Publishing|Morgan & Claypool|Springer, 2015
ISBN 10: 3031012801 ISBN 13: 9783031012808
Sprache: Englisch
Anbieter: moluna, Greven, Deutschland
Zustand: New. 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 II deals with more advanced material than Book I and is .
Verlag: Springer International Publishing AG, CH, 2015
ISBN 10: 3031012801 ISBN 13: 9783031012808
Sprache: Englisch
Anbieter: Rarewaves.com UK, London, Vereinigtes Königreich
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In den WarenkorbPaperback. Zustand: New. 1°. 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 II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology ofcompact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.
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In den WarenkorbHardback. Zustand: Very Good. Series: Studies in Advanced Mathematics. 279p sturdy hardback, grey laminated boards with red lettering, very good condition, minimal wear, tight binding, spine not creased, light marks to edges of textblock, pages clean and bright, text and mathematical symbols very clear and sharp, an excellent copy of a hard-to-find volume Language: English Weight (g): 594.
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