國立虎尾科技大學 |

Differential geometry = foundations of Cauchy-Riemann and pseudohermitian geometry.. (Book I-C) /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Differential geometry/ by Elisabetta Barletta ... [et al.].
其他題名:	foundations of Cauchy-Riemann and pseudohermitian geometry.
其他作者:	Barletta, Elisabetta.
出版者:	Singapore :Springer Nature Singapore : : 2025.,
面頁冊數:	xvi, 439 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Geometry, Differential. -
電子資源:	https://doi.org/10.1007/978-981-96-5020-0
ISBN:	9789819650200

Differential geometry = foundations of Cauchy-Riemann and pseudohermitian geometry.. (Book I-C) /
Differential geometryfoundations of Cauchy-Riemann and pseudohermitian geometry.(Book I-C) /[electronic resource] :by Elisabetta Barletta ... [et al.]. - Singapore :Springer Nature Singapore :2025. - xvi, 439 p. :ill., digital ;24 cm. - Infosys Science Foundation series in mathematical sciences,2364-4044. - Infosys Science Foundation series in mathematical sciences..

Cauchy-Riemann manifolds -- Pseudohermitian geometry -- Tangential Cauchy-Riemann complex -- Submanifolds of Hermitian and Sasakian manifolds.

This book, Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C), is the third in a series of four books presenting a choice of topics, among fundamental and more advanced, in Cauchy-Riemann (CR) and pseudohermitian geometry, such as Lewy operators, CR structures and the tangential CR equations, the Levi form, Tanaka-Webster connections, sub-Laplacians, pseudohermitian sectional curvature, and Kohn-Rossi cohomology of the tangential CR complex. Recent results on submanifolds of Hermitian and Sasakian manifolds are presented, from the viewpoint of the geometry of the second fundamental form of an isometric immersion. The book has two souls, those of Complex Analysis versus Riemannian geometry, and attempts to fill in the gap among the two. The other three books of the series are: Differential Geometry: Manifolds, Bundles, Characteristic Classes (Book I-A) Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B) Differential Geometry: Advanced Topics in Cauchy-Riemann and Pseudohermitian Geometry (Book I-D) The four books belong to an ampler book project "Differential Geometry, Partial Differential Equations, and Mathematical Physics", by the same authors, and aim to demonstrate how certain portions of differential geometry (DG) and the theory of partial differential equations (PDEs) apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG and PDEs machinery yet do not constitute a comprehensive treatise on DG or PDEs, but rather authors' choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions-isometric, holomorphic, and CR-and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.

ISBN: 9789819650200

Standard No.: 10.1007/978-981-96-5020-0doiSubjects--Topical Terms:

527830
Geometry, Differential.

LC Class. No.: QA641

Dewey Class. No.: 516.36

Differential geometry = foundations of Cauchy-Riemann and pseudohermitian geometry.. (Book I-C) /
LDR:03155nam a2200337 a 4500 001 1166936
003 DE-He213
005 20250712073512.0
006 m d
007 cr nn 008maaau
008 251217s2025 si s 0 eng d
020 $a 9789819650200 $q (electronic bk.)
020 $a 9789819650194 $q (paper)
024 7 $a 10.1007/978-981-96-5020-0 $2 doi
035 $a 978-981-96-5020-0
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 .D569 2025
245 0 0 $a Differential geometry $h [electronic resource] : $b foundations of Cauchy-Riemann and pseudohermitian geometry. $n (Book I-C) / $c by Elisabetta Barletta ... [et al.].
260 $a Singapore : $c 2025. $b Springer Nature Singapore : $b Imprint: Springer,
300 $a xvi, 439 p. : $b ill., digital ; $c 24 cm.
490 1 $a Infosys Science Foundation series in mathematical sciences, $x 2364-4044
505 0 $a Cauchy-Riemann manifolds -- Pseudohermitian geometry -- Tangential Cauchy-Riemann complex -- Submanifolds of Hermitian and Sasakian manifolds.
520 $a This book, Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C), is the third in a series of four books presenting a choice of topics, among fundamental and more advanced, in Cauchy-Riemann (CR) and pseudohermitian geometry, such as Lewy operators, CR structures and the tangential CR equations, the Levi form, Tanaka-Webster connections, sub-Laplacians, pseudohermitian sectional curvature, and Kohn-Rossi cohomology of the tangential CR complex. Recent results on submanifolds of Hermitian and Sasakian manifolds are presented, from the viewpoint of the geometry of the second fundamental form of an isometric immersion. The book has two souls, those of Complex Analysis versus Riemannian geometry, and attempts to fill in the gap among the two. The other three books of the series are: Differential Geometry: Manifolds, Bundles, Characteristic Classes (Book I-A) Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B) Differential Geometry: Advanced Topics in Cauchy-Riemann and Pseudohermitian Geometry (Book I-D) The four books belong to an ampler book project "Differential Geometry, Partial Differential Equations, and Mathematical Physics", by the same authors, and aim to demonstrate how certain portions of differential geometry (DG) and the theory of partial differential equations (PDEs) apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG and PDEs machinery yet do not constitute a comprehensive treatise on DG or PDEs, but rather authors' choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions-isometric, holomorphic, and CR-and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.
650 0 $a Geometry, Differential. $3 527830
650 1 4 $a Differential Geometry. $3 671118
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
700 1 $a Barletta, Elisabetta. $3 1488445
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Infosys Science Foundation series in mathematical sciences. $3 1486972
856 4 0 $u https://doi.org/10.1007/978-981-96-5020-0
950 $a Mathematics and Statistics (SpringerNature-11649)