語系:
繁體中文
English
說明(常見問題)
回圖書館
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Geometric realizations of curvature
~
Brozos-Vázquez, Miguel.
Geometric realizations of curvature
紀錄類型:
書目-電子資源 : 單行本
正題名/作者:
Geometric realizations of curvature/ Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic.
作者:
Brozos-Vázquez, Miguel.
其他作者:
Gilkey, Peter B.
出版者:
London :Imperial College Press, : 2012.,
面頁冊數:
1 online resource (ix, 252 p.) :ill. :
標題:
Curvature. -
電子資源:
http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc
ISBN:
9781848167421 (electronic bk.)
Geometric realizations of curvature
Brozos-Vázquez, Miguel.
Geometric realizations of curvature
[electronic resource] /Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic. - London :Imperial College Press,2012. - 1 online resource (ix, 252 p.) :ill. - ICP advanced texts in mathematics,v. 61753-657X ;. - Imperial College Press advanced texts in mathematics ;v. 6..
Includes bibliographical references and index.
A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature.
ISBN: 9781848167421 (electronic bk.)Subjects--Topical Terms:
247222
Curvature.
Index Terms--Genre/Form:
96803
Electronic books.
LC Class. No.: QA645 / .V39 2012eb
Dewey Class. No.: 515/.1
Geometric realizations of curvature
LDR
:02702cmm a2200253Ma 4500
001
137463
006
m o u
007
cr cn|||||||||
008
160114s2012 enka ob 001 0 eng d
020
$a
9781848167421 (electronic bk.)
020
$a
1848167423 (electronic bk.)
020
$z
1848167415
020
$z
9781848167414
035
$a
ocn797852271
040
$a
E7B
$c
E7B
$d
OCLCO
$d
YDXCP
$d
I9W
$d
OCLCQ
$d
DEBSZ
$d
OCLCQ
$d
CDX
049
$a
FISA
050
1 4
$a
QA645
$b
.V39 2012eb
082
0 4
$a
515/.1
$2
23
100
1
$a
Brozos-Vázquez, Miguel.
$3
247219
245
1 0
$a
Geometric realizations of curvature
$h
[electronic resource] /
$c
Miguel Brozos Vázquez, Peter B. Gilkey, Stana Nikcevic.
260
$a
London :
$c
2012.
$b
Imperial College Press,
300
$a
1 online resource (ix, 252 p.) :
$b
ill.
490
1
$a
ICP advanced texts in mathematics,
$x
1753-657X ;
$v
v. 6
504
$a
Includes bibliographical references and index.
520
$a
A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer-Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri-Vanhecke decomposition, the Gray-Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature.
650
0
$a
Curvature.
$3
247222
650
0
$a
Geometry.
$3
99757
655
0
$a
Electronic books.
$2
local.
$3
96803
700
1
$a
Gilkey, Peter B.
$3
247220
700
1
$a
Nikcevic, Stana.
$3
247221
830
0
$a
Imperial College Press advanced texts in mathematics ;
$v
v. 6.
$3
247218
856
4 0
$u
http://www.worldscientific.com/worldscibooks/10.1142/P787#t=toc
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼
登入