Karl Otto Heinrich Liebmann (* 22. October 1874 in
Strasbourg
Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the Eu ...
; † 12. June 1939 in
Munich-Solln) was a German
mathematician and
geometer.
Life
Liebmann was the son of
Otto Liebmann (1840–1912), a
Jewish
neo-Kantian philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
professor in
Jena. Heinrich studied from 1895 to 1897 at the universities
Leipzig,
Jena and
Göttingen. In 1895 he was awarded the
doctorate under
Carl Johannes Thomae with the subject ''Die einzweideutigen projektiven Punktverwandtschaften der Ebene'' and passed the
Lehramtsprüfung in 1896. In 1897 he was an assistant in Göttingen and in 1898 in Leipzig, where he was
habilitated
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...
on the subject ''Über die Verbiegung der geschlossenen Flächen positiver Krümmung''. In this work, among other things, he stated
Liebmann's theorem
In differential geometry, the Gaussian curvature or Gauss curvature of a surface at a point is the product of the principal curvatures, and , at the given point:
K = \kappa_1 \kappa_2.
The Gaussian radius of curvature is the reciprocal of .
F ...
in
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
.
In 1905, he became extraordinary professor in Leipzig, in 1910 extraordinary professor at the
Technischen Hochschule München, where he became professor in 1915. In 1920 he followed
Paul Stäckel
Paul Gustav Samuel Stäckel (20 August 1862, Berlin – 12 December 1919, Heidelberg) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he ...
as professor at the
Universität Heidelberg
}
Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, ...
, where he became
rector
Rector (Latin for the member of a vessel's crew who steers) may refer to:
Style or title
*Rector (ecclesiastical), a cleric who functions as an administrative leader in some Christian denominations
*Rector (academia), a senior official in an edu ...
in 1926 and
dean of the faculty of mathematics and natural science in 1923/1924 as well as in 1928/1929. In 1935 he asked for retirement due to political pressure of the
national socialists because of Liebmann's
Jewish ancestry. He and his colleague
Arthur Rosenthal were boycotted in his faculty. He spent his last years in Munich.
In 1913 he married his first wife Natalie Liebmann, née Kraus († 1924), who was the daughter of Karl Kraus, professor of agricultural science in Munich. After the death of his first wife he married Helene Ehlers. He had four children.
Liebmann was concerned, among other things, with
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
and
non-Euclidean geometry. He discovered the construction of a
triangle from its three angles by circle and ruler within
hyperbolic geometry. In his habilitation, he showed that a convex closed surface cannot be bent (theorem of Minding and
Liebmann's theorem
In differential geometry, the Gaussian curvature or Gauss curvature of a surface at a point is the product of the principal curvatures, and , at the given point:
K = \kappa_1 \kappa_2.
The Gaussian radius of curvature is the reciprocal of .
F ...
). He translated the works of
Nikolai Lobachevsky into German.
Liebmann was a member of the
Saxon Academy of Sciences
The Saxon Academy of Sciences and Humanities in Leipzig (german: Sächsische Akademie der Wissenschaften zu Leipzig) is an institute which was founded in 1846 under the name ''Royal Saxon Society for the Sciences'' (german: Königlich Sächsische G ...
, the
Bavarian Academy of Sciences and Humanities
The Bavarian Academy of Sciences and Humanities (german: Bayerische Akademie der Wissenschaften) is an independent public institution, located in Munich. It appoints scholars whose research has contributed considerably to the increase of knowledg ...
and the
Heidelberg Academy of Sciences and Humanities.
[See Gabriele Dörflinger]
''Mathematik in der Heidelberger Akademie der Wissenschaften''
2014. S. 47–49.
Works (selection)
* ''Die einzweideutigen projektiven Punktverwandtschaften der Ebene.'' Jena, 1895
Digitalisat Univ. Heidelberg
* ''Über die Verbiegung der geschlossenen Flächen positiver Krümmung'' Leipzig 1900
Digitalisat Univ. Heidelberg
* ''Lehrbuch der Differentialgleichungen''. Leipzig 1901
* ''Die nichteuklidische Geometrie. Historisch kritische Darstellung ihrer Entwicklung''. Berlin 1908, 1912, 1923 (zusammen mit
Roberto Bonola)
* ''Synthetische Geometrie''. Leipzig 1934
* ''Nichteuklidische Geometrie.'' Leipzig 1905.
* ''Das Problem der Kreisteilung.'' Leipzig/Berlin 1913.
* ''Die Berührungstransformationen, Geschichte und Invariantentheorie.'' Leipzig 1914.
* ''Die Sätze von Lie und Gambier über Kurven deines Linienkomplexes.'' Berlin 1928.
* ''N. J. Lobatschefskijs imaginäre Geometrie und Anwendung der imaginären Geometrie auf einige Integrale'', 1904
„Eine neue Eigenschaft der Kugel“, Mitteilungen Akademie Göttingen 1899''Die elementaren Konstruktionen der nichteuklidischen Geometrie'', Jahresbericht DMV 1911„Notwendigkeit und Freiheit in der Mathematik“, Jahresbericht DMV 1905, Antrittsvorlesung Leipzig„Neuer Beweis des Mindingschen Satzes“, Jahresbericht DMV 1903„Neuer Beweis des Satzes, dass eine geschlossene konvexe Fläche sich nicht verbiegen läßt“, Mathematische Annalen Bd.54, 1901„Geometrische Theorie der Differentialgleichungen“, Enzyklopädie der Mathematischen Wissenschaften 1914„Berührungstransformationen“, Enzyklopädie der Mathematischen Wissenschaften 1914
Bibliography
*
*
Siegfried Gottwald, Hans J. Ilgauds, Karl H. Schlote (Hrsg.): ''Lexikon bedeutender Mathematiker''. Bibliographisches Institut, Leipzig 1990, .
* Gabriele Dörflinger: ''Heinrich Liebmann – Mathematiker''. In: ''
Badische Biographien'', Neue Folge, Band 6 (2011), S. 258–259.
Manuskript.
* Dorothee Mußgnug: ''Die vertriebenen Heidelberger Dozenten : zur Geschichte der Ruprecht-Karls-Universität nach 1933.'' Heidelberg 1988
* Heinrich Liebmann: ''Die Notwendigkeit der Freiheit in der Mathematik'' (Leipziger Antrittsvorlesung) in: Herbert Beckert, Walter Purkert ''Leipziger mathematische Antrittsvorlesungen. Auswahl aus den Jahren 1869-1922'', B. G. Teubner, Leipzig 1987 (mit Biografie)
External links
Heinrich Liebmann at University Leipzig
References
{{DEFAULTSORT:Liebmann, Heinrich
1874 births
1939 deaths
19th-century German mathematicians
20th-century German mathematicians
University of Jena alumni
Academic staff of Leipzig University
Academic staff of the Technical University of Munich
Academic staff of Heidelberg University