Complex Differential Geometry (AMS/IP Studies in Pure Mathematics) - Tapa blanda

American Mathematical Society

 
9780821829608: Complex Differential Geometry (AMS/IP Studies in Pure Mathematics)
Tapa blanda
ISBN 10: 0821829602 ISBN 13: 9780821829608
Editorial: American Mathematical Society, 2002

Sinopsis

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds.The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classification theory, providing readers with some concrete examples of complex manifolds. The last part is the main purpose of the book; in it, the author discusses metrics, connections, curvature, and the various roles they play in the study of complex manifolds. A significant amount of exercises are provided to enhance student comprehension and practical experience.

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Reseña del editor

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds.The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classification theory, providing readers with some concrete examples of complex manifolds. The last part is the main purpose of the book; in it, the author discusses metrics, connections, curvature, and the various roles they play in the study of complex manifolds. A significant amount of exercises are provided to enhance student comprehension and practical experience.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
American Mathematical Society
Año de publicación
2002
Idioma
Inglés
ISBN 10 
0821829602
ISBN 13 
9780821829608
Encuadernación
Tapa blanda
Número de páginas
264
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9780821821633: Complex Differential Geometry: No. 18 (AMS/IP Studies in Advanced Mathematics)

Edición Destacada

ISBN 10:  0821821636 ISBN 13:  9780821821633
Editorial: American Mathematical Society, 2000
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