Frank Löbell

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Frank Löbell, 1930 in Jena

Frank Richard Löbell (born May 11, 1893 in Tandjong Morawa on Sumatra , † May 31, 1964 in Munich ) was a German mathematician who worked primarily in the field of geometry .

education

Löbell suffered from malaria until he was 10 years old . When his father fell ill and decided to return to Germany with his family, the latter died on the sea voyage when his son Frank Löbell was five years old. The mother moved first to Ludwigsburg and then to Strasbourg , which at that time belonged to Germany. Löbell went to school there and passed the final examination at the Protestant grammar school in 1912.

From 1912 to 1918 Löbell studied mathematics and physics at the University of Strasbourg . He continued his studies from 1918-20 at the University of Freiburg , graduating from the University of Tübingen .

In 1920 he passed the first and in 1921 the second service examination for the higher teaching post in Württemberg.

In 1926 he did his doctorate with Karl Kommerell in Tübingen with the thesis The everywhere regular surfaces of fixed curvature , 92 pages. The suggestion for this work came from Friedrich Schur; Gerhard Hessenberg gave support.

In 1928 he completed his habilitation at the TH Stuttgart with investigations into geodetic lines on Clifford-Klein surfaces.

Professional activities

From 1922 to 1928 he was assistant to Wilhelm Kutta at the TH Stuttgart, 1928–1930 private lecturer at the TH Stuttgart.

From 1931 to 1934 he was professor of geometry at the TH Stuttgart, from 1934 until his retirement in 1959 he was a full professor of geometry at the TH Munich . In addition to the course lectures in descriptive geometry, he regularly held lectures there, including a. on differential geometry, basics of geometry, non-Euclidean geometry, synthetic (projective) geometry, geometric constructions and map projections.

After the collapse of the Third Reich, the university and the badly damaged floors of the chair for geometry were in a deplorable condition. The reconstruction of the university and its institutes, the continuation of teaching, the restoration of its internal order and the structure of self-administration represented many and difficult tasks. Löbell devoted himself to mastering them with all his strength.

In 1946 he became dean and 1947/1948 vice dean of the Faculty of General Sciences. The trust of his colleagues placed him in the position of Vice-Rector of the TH Munich in 1949/50. Since 1947 he was a full member of the Bavarian Academy of Sciences , in which he temporarily held the office of class secretary for the mathematical and scientific class, he was involved in several commissions and in the publication of the collected mathematical writings of Constantin Carathéodory . In 1960 he became a member of the Kepler Society.

Although his weakened health had long prevented him, he continued to work scientifically until his death. The completion of the new edition of the non-Euclidean geometry by Baldus-Löbell (Göschen Collection) was his last work.

Private life

He was not spared severe strokes of fate. During the Second World War he lost his apartment with the entire library in a bomb attack. His eldest son has been missing since the fighting in Pomerania . After a short, serious illness, the youngest son died soon after the war at the age of 15.

Works

Löbell researched mainly in the field of geometry, u. a. in the following areas:

  • I. Non-Euclidean Geometry
    • a) General (also for absolute geometry)
      • 9 works, including the publication and revision of the Göschenbändchen Non-Euclidean Geometry by Richard Baldus.
    • b) On the Clifford-Klein space problem
      • 9 Work on the surfaces of constant negative Gaussian curvature in three-dimensional space, on which the non-Euclidean (hyperbolic) geometry applies locally.
  • II. Three-dimensional differential geometry
    • a) General area theory
      • 23 works in which mostly the “natural method” is applied with the help of accompanying driving.
    • b) Mapping of surfaces on top of one another
      • 17 works.
  • III. various
    • 11 math and
    • 3 biographical works.

More details with a list of all publications by Frank Löbell can be found in the obituary in the annual report of the German Mathematicians Association Volume 70 (see below).

List of publications

Abbreviations:

ADM Archives of Mathematics
BS reports of the mathematical-physical class of the Saxon Academy of Sciences
CR Comptes Rendus
FUF research and advances
JDMV annual report of the German Mathematicians Association
JM Journal for Pure and Applied Mathematics
MFM monthly books for mathematics
MA Mathematical Annals
MZ Mathematical Journal
SBB meeting reports of the Bavarian Academy of Sciences, math and science class
SBP meeting reports of the Prussian Academy of Sciences, physical-mathematical class
UF From teaching and research
ZAMM Journal for Applied Mathematics and Mechanics
ZMNU Journal for mathematics and science teaching

On non-Euclidean geometry

General
  • "Maps" of the non-Euclidean plane. JDMV 54 (1950) 4-23
  • A real interpretation of the complex vectors. (Interpretation as straight line) MZ 52 (1950) 759-769.
  • Short report on Darmstadt's lecture (on the content of [2]). ZAMM 30 (1950) 287
  • The right-angled five-sided as the basic figure of trigonometry. UF (Stuttgart) 5 (1933), 112-118 and 161-167.
  • A generalization of the Pentagramma Mirificum. (Revised with complex vectors.) MZ 53 (1950) 236–243.
  • The “core” as the basis of complex vectors. MZ 54 (1951) 129-135.
  • The Hjelmslev Middle Line Theorem and Related Theorems. MFM 65: 249-251 (1961).
  • Note on some theorems of triangles in absolute geometry. MFM 67 (1963), 101-103
  • Publication of the 3rd and 4th edition of Göschenbändchen 970 on non-Euclidean geometry. Hyperbolic geometry of the plane. By Richard Baldus. Verlag Walter de Gruyter 1953, reviewed and edited by F. Löbell. 70 Fig. And 1964, edited and supplemented by F. Löbell.
Especially on the Clfford-Klein problem of space
  • The everywhere regular surfaces of fixed curvature. Dissertation 1926. Tübingen 1927. 92 pages.
  • About the geodetic lines of the Clifford-Klein planes. MZ 30, 572-607. (Main part of the Habil. 1928).
  • Généralisation d'un théoréme de HA Black. CR. 188: 372-375 (1929).
  • A theorem on the unambiguous movements of Clifford-Klein surfaces. (From the habilitation thesis.) JM 162 (1930) 114–124; 163: 134 (1930).
  • On the question of the structure of the closed geodetic lines of the open Clifford-Klein surfaces of positive characteristics. JM 162: 125-131 (1930).
  • An example on the question of the course of the closed geodetic lines in a Clifford-Klein surface. JDMV 40 (1931), 69-74.
  • Some properties of the straight line in certain Clifford-Kleinian spaces. SBP 1930, 556-558.
  • Examples of closed three-dimensional Clifford-Kleinian spaces of negative curvature. BS 83 (1931) 167-174.
  • For the construction of closed Clifford-Klein spaces of negative curvature. SBB 1955, 175-185.

Differential geometry

General (according to the "natural" method)
  • Kinematic foundation of curve and surface theory. JDMV 39 (1930) 168-182.
  • The movement of the accompanying triangle. JDMV 51 (1941) 148-150.
  • The basic equations of area theory and their expression using integral theorems. SBB 1929, 165-173.
  • A sentence about express lines. JDMV 48 (1938) 172-175.
  • A spatial generalization of the four-vertex theorem. JDMV 49 (1939) 140-143.
  • To the differential geometry of the rule shares. JDMV 51 (1941) 2nd section 29–…
  • From the differential geometry of the screw shares. (Dual vectors). Festschrift of the Technical University of Stuttgart. Berlin 1929, 210-226.
  • Basics of a differential theory of somebody congruence. SBB 1942, 1-16.
  • A vectorial side piece to the Gauss-Bonnet integral theorem. SBB 1947, 119-128.
  • Remarks on the proof of the Gauss-Bonnet theorem. SBB 1942, 25-39.
  • An expression for the amount of curvature. (Application in [30]). SBB 1948, 8.
  • Surfaces with a given vectorial differential invariant. SBB 1952, 99-101.
  • Natural geometry of the curve congruences. MZ 56 (1952) 208-218
  • Relationship between vector analysis and curvature theory of curve congruences. SBB 1958, 73-79.
  • Line element functions and geodetic derivatives in area theory. MA 121 (1950) 427-445.
  • Relationships between geodetic derivatives of curvature quantities SBB 1949, 37–40.
  • Variation of curve integrals via line element functions. SBB 1954, 1-3.
  • Remarks on a Beltrami-Bonnet Relationship. MFM 66: 215-219 (1962).
  • On the question of the interchangeability of geodetic directional derivations. MA 122: 152-156 (1950).
  • The integrability condition for position functions in natural area theory. MA 124 (1951) 151-157.
  • The integrability condition for position functions in non-integrable reference systems. SBB 1956, 33-39.
  • Directional transmissions on a surface. JDMV 55 (1952) 89-117.
  • Criteria for the integrability of directional transmissions in surfaces. SBB 1953, 141-148.
About images of surfaces on top of each other
  • General theory of surface mapping. News from the Reich Surveying Service 1942, 299–307.
  • On the theory of surface mapping. MZ 49 (1943) 427-440.
  • From the theory of surface mapping. ADM 1 (1948) 73-76.
  • Some concepts of the theory of surface formations. JDMV 54 (1951) 2nd Dept., 32-34.
  • Differential invariants in surface images. SBB 1943, 217-237.
  • Area mappings with a common invariant system. MA 120: 23-35 (1947).
  • About some integral variants that occur in surface mapping. SBB 1944, 107-132.
  • Considerations about surface mapping. SBB 1946, 175-183; 1947, 25-33; 1947, 35-43; 1947, 77-80; 1947, 179-186; 1948, 71-79; 1948, 227-234; 1948, 335-339; 1954, 135-148.
  • Integrability conditions in the theory of surface mapping. SBB 1951, 11-18.
  • A differential geometric operator in the theory of surface mapping. ADM 2 (1949/50) 17-23.
  • Weingarten's characteristic equation and a similar differential equation in the theory of surface mapping. ADM 2 (1949/50) 96-102.
  • Relationships between the theories of curve congruence and surface mapping. SBB 1952, 47-50.
  • Differential forms in the theory of surface mapping. SBB 1954, 149-157.
  • Dyads in the theory of surface mapping. SBB 1954, 335-345.
  • The influence of a surface transformation on the geodetic curvatures. SBB 1957, 15-24.
  • True-to-scale change of geodetic curvatures in surface images. SBB 1962, 9-20.
  • Coupled directional transmissions on pairs of surfaces. SBB 1960, 263-268.

various

Mathematical work
  • Guide to Descriptive Geometry. (The most important terms, sentences and procedures, for use next to the lecture.) Scripts of the Munich Student Union 1949, 1953, 1958.
  • A construction of the pair of points that lie harmoniously with two given pairs of points of the complex number plane. JDMV 36: 364 (1927); 38 (1929), 190.
  • A contribution to the determination of the deformation of an elastic membrane under the influence of given external forces. ZAMM 7 (1927) 463-469.
  • To the problem of the main lines of shear stress in plastic materials. ZAMM (1929) 213-224.
  • A remark on an elementary geometric problem. ZMNU 59 (1928) 345-347.
  • A solution to the cubic equation. JDMV 38 (1929) 152-153.
  • Tufts of threads and their invariants. JM 164 (1931) 64-66.
  • Geometry, reality and intuition. FUF 19 (1943) 174-176.
  • Considerations on the transmission of routes in Euclid. FUF 1919 (1943) 320-321.
  • One possibility of classifying the calculus of Pfaff's forms in Graßmnn's theory of expansion. SBB 1952, 8.
  • A note on Kepler's equation. SBB meeting on December 6, 1963.
Biographical work
  • Viktor Schlegel on his 100th birthday. Press office of the Reich Central for Scientific Reporting 1943. May, 3, 16-17.
  • Obituary for Martin Näbauer. JBB 1951, 149-152.
  • Obituary for Konrad Knopp. JBB 1958, 187-189.

literature

Web links

personal data
SURNAME Löbell, Frank
ALTERNATIVE NAMES Löbell, Frank Richard
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH May 11, 1893
PLACE OF BIRTH Tandjong Morawa in Sumatra
DATE OF DEATH May 31, 1964
Place of death Munich