國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Differential geometry and lie groups...

Gallier, Jean.

Differential geometry and lie groupsa second course /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Differential geometry and lie groupsby Jean Gallier, Jocelyn Quaintance.
其他題名:	a second course /
作者:	Gallier, Jean.
其他作者:	Quaintance, Jocelyn.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	xiv, 620 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Geometry, Differential.
電子資源:	https://doi.org/10.1007/978-3-030-46047-1
ISBN:	9783030460471$q(electronic bk.)

Differential geometry and lie groupsa second course /
Gallier, Jean.

Differential geometry and lie groupsa second course /[electronic resource] :by Jean Gallier, Jocelyn Quaintance. - Cham :Springer International Publishing :2020. - xiv, 620 p. :ill., digital ;24 cm. - Geometry and computing,v.131866-6795 ;. - Geometry and computing ;7..

1. Tensor Algebras -- 2. Exterior Tensor Powers and Exterior Algebras -- 3. Differential Forms -- 4. Distributions and the Frobenius Theorem -- 5. Integration on Manifolds -- 6. Spherical Harmonics and Linear Representations -- 7. Operators on Riemannian Manifolds -- 8. Bundles, Metrics on Bundles, Homogeneous Spaces -- 9. Connections and Curvature in Vector Bundles -- 10. Clifford Algebras, Clifford Groups, Pin and Spin.

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors' companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.

ISBN: 9783030460471$q(electronic bk.)

Standard No.: 10.1007/978-3-030-46047-1doiSubjects--Topical Terms:

182610
Geometry, Differential.

LC Class. No.: QA641

Dewey Class. No.: 516.36

Differential geometry and lie groupsa second course /
LDR:03019nmm a2200337 a 4500 001 585393
003 DE-He213
005 20201228113926.0
006 m d
007 cr nn 008maaau
008 210311s2020 sz s 0 eng d
020 $a 9783030460471$q(electronic bk.)
020 $a 9783030460464$q(paper)
024 7 $a 10.1007/978-3-030-46047-1 $2 doi
035 $a 978-3-030-46047-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA641
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 516.36 $2 23
090 $a QA641 $b .G168 2020
100 1 $a Gallier, Jean. $3 510872
245 1 0 $a Differential geometry and lie groups $h [electronic resource] : $b a second course / $c by Jean Gallier, Jocelyn Quaintance.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xiv, 620 p. : $b ill., digital ; $c 24 cm.
490 1 $a Geometry and computing, $x 1866-6795 ; $v v.13
505 0 $a 1. Tensor Algebras -- 2. Exterior Tensor Powers and Exterior Algebras -- 3. Differential Forms -- 4. Distributions and the Frobenius Theorem -- 5. Integration on Manifolds -- 6. Spherical Harmonics and Linear Representations -- 7. Operators on Riemannian Manifolds -- 8. Bundles, Metrics on Bundles, Homogeneous Spaces -- 9. Connections and Curvature in Vector Bundles -- 10. Clifford Algebras, Clifford Groups, Pin and Spin.
520 $a This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors' companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
650 0 $a Geometry, Differential. $3 182610
650 0 $a Topological groups. $3 541301
650 0 $a Lie groups. $3 190898
650 0 $a Computer science $x Mathematics. $3 181991
650 1 4 $a Differential Geometry. $3 273785
650 2 4 $a Topological Groups, Lie Groups. $3 273787
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 274020
700 1 $a Quaintance, Jocelyn. $3 876392
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Geometry and computing ; $v 7. $3 560055
856 4 0 $u https://doi.org/10.1007/978-3-030-46047-1
950 $a Mathematics and Statistics (SpringerNature-11649)