Quadratic Differentials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1984
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics
5 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A quadratic differential on aRiemann surface is locally represented by a ho lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the surface, with singularities at the critical points, i.e. the zeros and poles of the differential. The integral curves of this field are called the trajectories of the differential. A large part of this book is about the trajectory structure of quadratic differentials. There are of course local and global aspects to this structure. Be sides, there is the behaviour of an individual trajectory and the structure deter mined by entire subfamilies of trajectories. An Abelian or first order differential has an integral or primitive function is in general not single-valued. In the case of a quadratic on the surface, which differential, one first has to take the square root and then integrate. The local integrals are only determined up to their sign and arbitrary additive constants. However, it is this multivalued function which plays an important role in the theory; the trajectories are the images of the horizontals by single valued branches of its inverse |
| Beschreibung: | 1 Online-Ressource (XII, 186 p) |
| ISBN: | 9783662024140 9783642057236 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-662-02414-0 |
Internformat
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Strebel, Kurt |
| author_facet | Strebel, Kurt |
| author_role | aut |
| author_sort | Strebel, Kurt |
| author_variant | k s ks |
| building | Verbundindex |
| bvnumber | BV042423194 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-02414-0 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783662024140 9783642057236 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858611 |
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| publishDate | 1984 |
| publishDateSearch | 1984 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics |
| spelling | Strebel, Kurt Verfasser aut Quadratic Differentials by Kurt Strebel Berlin, Heidelberg Springer Berlin Heidelberg 1984 1 Online-Ressource (XII, 186 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics 5 0071-1136 A quadratic differential on aRiemann surface is locally represented by a ho lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the surface, with singularities at the critical points, i.e. the zeros and poles of the differential. The integral curves of this field are called the trajectories of the differential. A large part of this book is about the trajectory structure of quadratic differentials. There are of course local and global aspects to this structure. Be sides, there is the behaviour of an individual trajectory and the structure deter mined by entire subfamilies of trajectories. An Abelian or first order differential has an integral or primitive function is in general not single-valued. In the case of a quadratic on the surface, which differential, one first has to take the square root and then integrate. The local integrals are only determined up to their sign and arbitrary additive constants. However, it is this multivalued function which plays an important role in the theory; the trajectories are the images of the horizontals by single valued branches of its inverse Mathematics Functions of complex variables Functions of a Complex Variable Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Meromorphe Funktion (DE-588)4136862-9 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Quadratisches Differential (DE-588)4176565-5 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s Quadratisches Differential (DE-588)4176565-5 s 1\p DE-604 Holomorphe Funktion (DE-588)4025645-5 s 2\p DE-604 Meromorphe Funktion (DE-588)4136862-9 s 3\p DE-604 https://doi.org/10.1007/978-3-662-02414-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Strebel, Kurt Quadratic Differentials Mathematics Functions of complex variables Functions of a Complex Variable Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd Meromorphe Funktion (DE-588)4136862-9 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Quadratisches Differential (DE-588)4176565-5 gnd |
| subject_GND | (DE-588)4049991-1 (DE-588)4136862-9 (DE-588)4025645-5 (DE-588)4176565-5 |
| title | Quadratic Differentials |
| title_auth | Quadratic Differentials |
| title_exact_search | Quadratic Differentials |
| title_full | Quadratic Differentials by Kurt Strebel |
| title_fullStr | Quadratic Differentials by Kurt Strebel |
| title_full_unstemmed | Quadratic Differentials by Kurt Strebel |
| title_short | Quadratic Differentials |
| title_sort | quadratic differentials |
| topic | Mathematics Functions of complex variables Functions of a Complex Variable Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd Meromorphe Funktion (DE-588)4136862-9 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Quadratisches Differential (DE-588)4176565-5 gnd |
| topic_facet | Mathematics Functions of complex variables Functions of a Complex Variable Mathematik Riemannsche Fläche Meromorphe Funktion Holomorphe Funktion Quadratisches Differential |
| url | https://doi.org/10.1007/978-3-662-02414-0 |
| work_keys_str_mv | AT strebelkurt quadraticdifferentials |