Hermann Karcher

Mathematisches Institut der Universität Bonn
Endenicher Allee 60
53115 Bonn

Arbeitszimmer: Endenicher Allee 60, Zimmer 3.007
Telefon: +49 228 73-2841, Geschäftszimmer: 73-2204

Hopf-fibered linked Tori aus 3D-XplorMath
HopfFibered.png (52705 Byte)

Image sequences made with this program are in virtualmathmuseum.org

e-mail:Meine email Adresse
(.gif, please do not store in computer readable lists.)
I continue to use this e-mail address.
I no longer check my spam folder.
Therefore some good mail may get lost.


Meine Arbeitsgebiete:
Riemannsche Geometrie und Untermannigfaltigkeiten.

The interactive Plane Curves and Polyhedra of the museum are here (2020)
PLnCrvPol.png (1125579 Byte)

--------------------------- Correction (2014) ----------------------------

Wikipedia falsely writes: Karcher means are a closely related construction named after Hermann Karcher.

True is: Karcher mean is the renaming of the Riemannian Center of Mass construction developed by Karsten Grove and Hermann Karcher in: How to conjugate C1-close group actions, Math.Z. 132, 1973, pp 11-20.

My 1977 paper with Riemannian Center of Mass in the title is more easily found by google. But that does not justify such a renaming. There I also quote: Grove, K., Karcher, H., Ruh, E. A., Jacobi fields and Finsler metrics on compact Lie Groups ..., Math. Ann. 211, 1974, pp. 7-21, where the center is defined on SO(n) on much larger sets than can be done with their Riemannian metric. In Buser, P., Karcher, H., Gromov's Almost Flat Manifolds, Soc. Mat. France, Astérisque 81, 1981, the center is defined on nilpotent Lie groups just using their connection, as in the Euclidean affine case. On spheres the squared distance does not work so well since its Hessian has different eigenvalues in radial and tangential direction. It is easier, and even explicit, to use 1- cos(d(.,p)) instead, since the minimum point of this function is the Euclidean center projected from the midpoint back to the sphere. In Chern's book Global Differential Geometry, MAA Studies in Mathematics, Vol 27, 1989, my article Riemannian Comparison Constructions explains about such modified distance functions. The book is out of print, but google finds my contribution on my Homepage.

For more details see: Riemannian Center of Mass and so called karcher mean (or: http://arxiv.org/abs/1407.2087)


Some Published and Unpublished Manuscripts, small texts are still added (2019).

Information zu Vorlesungen WS 99/00 bis WS 03/04, Aufgaben, Bilder, Texte.

Crystal Cove State Park: Photobook (60 MB, 2011) of its fascinating Geology.


Hier finden Sie Informationen über
unser Visualisierungsprogramm.

Dessen Homepage ist:
Die Museumsseite Raumkurven dazu ist: http://virtualmathmuseum.org/SpaceCurves/

Das nebenstehende Bild ist eine unveröffentlichte Raumkurve konstanter Krümmung aus 3D-XplorMath. Die dazugehörige Dokumentation kann hier angesehen werden.
Siehe auch: Closed Constant Curvature Space Curves, oder http://arxiv.org/abs/2004.10284

Eine Hypertextdokumentation aller mathematischen Objekte unseres Programms steht zur Verfügung.

Frenet Röhre um Raumkurve konstanter Krümmung
ConstantCurv5_2.png (25533 Byte)


Ich prüfe seit 2007 nicht mehr.

Aus der Zeit vor der Bologna-Reform: Ratschläge für Prüfungen

Zu meinen Matlabkursen.

Hochschulreform von außen und innen (analysis concepts).

Geometrisches Geschenk zu meinem 60. Geburtstag.


Am 13.5.02 war die Ehrenpromotion von Frau Prof. Dr. Olga A. Ladyzhenskaya. Verbunden damit war die Abschlußtagung (14.5.02) des SFB256.

Professor Dr. Olga A. Ladyzhenskaya, 7.3.1922 - 11.1.2004