Selected Papers of Wilhelm P.A. Klingenberg

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World Scientific, 1991 - Mathematics - 532 pages
This set of selected papers of Klingenberg covers some of the important mathematical aspects of Riemannian Geometry, Closed Geodesics, Geometric Algebra, Classical Differential Geometry and Foundations of Geometry of Klingenberg. Of significance were his contributions to Riemannian Geometry in the Large which opened a new area in Global Riemannian Geometry. He also introduced the Hilbert manifold of closed curves of class H1 on a Riemannian manifold. In connection with his work in closed geodesics, he became interested in the properties of the geodesic flow. Classical results from dynamical systems became useful tools for the study of closed geodesics. He was also credited for drawing closer together Riemannian Geometry and Hamiltonian systems, which had developed separately since the time of H Poincar .Besides publishing research papers, Klingenberg also wrote a dozen books and lecture notes, among which is the important reference work ?Riemannsche Geometrie im Gro?en?.
 

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Contents

4 Uber das Einspannungsproblem in der projektiven und affinen Differentialgeometrie
3
26 Neue Ergebnisse iiber konvexe Flachen
28
36 Die Struktur der linearen Gruppe über einem nichtkommutativen
36
78 Closed curves on 52 with bounded winding number
48
Foundation of Geometry
59
5 Beziehungen zwischen einigen affinen SchlieBungssatzen
61
8 Eine Begriindung der hyperbolischen Geometric
85
15 Beweis des Desarguesschen Satzes aus der Reidemeisterfigur und verwandte Satze
102
29 Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung
286
33 On compact Kaehlerian manifolds with positive holomorphic Curvature
294
40 Manifolds with restricted conjugate locus
301
II
322
52 Geodätischer Flu auf Mannigfaltigkeiten vom hyperbolischen Typ
332
53 Generic properties of geodesic flows with F Takens
352
58 Riemannian manifolds with geodesic flow of Anosov Type
364
70 Injectivity radius estimate for 14pinched manifolds with T Sakai
377

18 Projektive Geometrien mit Homomorphismus
120
Geometric Algebra
141
7 Sopra il numero degli ordinamenti di un corpo
143
9 Paare symmetrischer und alternierender Formen zweiten Grades
145
11 Uber die Arfsche Invariante quadratischer Formen mod 2
161
17 Die Anzahl der Nullstellen eines Polynoms in Gebieten mit stiickweise rationalen Randkurven
163
30 Lineare Gruppen iiber Lokalen Ringen
176
34 Orthogonale Gruppen iiber Lokalen Ringen
193
35 Projektive Geometric und Lineare Algebra iiber Verallgemeinerten Bewertungsringen
233
39 Symplectic groups over local rings
251
Riemannian Geometry
261
23 Eine Kennzeichnung der Riemannschen sowie der Hermiteschen Mannigfaltigkeiten
263
25 Contributions to Riemannian geometry in the large
273
Closed Geodesics
383
47 The space of closed curves on the sphere
385
48 Simple closed geodesics on pinched spheres
406
49 Closed geodesics
414
50 The space of closed curves on a projective space
438
61 Der Indexsatz für geschlossene Geodätische
459
71 Über die Existenz unendlich vieler geschlossener Geodätischer
485
77 Homology generated by iterated closed geodesics with V Bangert
508
Curriculum Vitae
519
Numbers in brackets refer to the bibliography on pp 523529
523
List of PhD theses written under the supervision of W P A Klingenberg
531
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