Thesis (Th. D.)--Rijksuniversiteit, Utrecht, 1957. / Summary in English. Includes bibliographical references (p. [109]-111) and index.

Thesis (Th. D.)--Rijksuniversiteit, Utrecht, 1957. / Summary in English. Includes bibliographical references (p. [109]-111) and index.

Thèse présentée à la Faculté de lettres de Paris ...

Thèse présentée à la Faculté de lettres de Paris ...

Inaug.-Diss.--Halle. / Cover title. Vita. Bibliography: p. [93]-94.

Texte remanié de: Thèse de doctorat--Histoire--Bordeaux 3, 2001. Titre de soutenance : Georges Bonnet (1889-1973), étude biographique. / Bibliogr. p. 341-351. Index.

Inaug.-diss.--Leipzig. / Vita. "Literatur": p. [118]-120.

The principal aim of this paper is to give an example of the Gauss-Bonnet Theorem together with its anew structure by using connection and curvature matrices with stereographic projection on the unit 2-sphere, S². We determine an orthonormal basis by applying stereographic projection on S² and we obtain the area of the unit 2 -sphere S² computing connection and curvature matrices.

From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.

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