Author | Hopf, Heinz. author |
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Title | Differential Geometry in the Large [electronic resource] : Seminar Lectures New York University 1946 and Stanford University 1956 / by Heinz Hopf |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/3-540-39482-6 |
Descript | VIII, 192 p. online resource |
Selected Topics in Geometry -- The Euler Characteristic and Related Topics -- Selected Topics in Elementary Differential Geometry -- The Isoperimetric Inequality and Related Inequalities -- The Elementary Concept of Area and Volume -- Differential Geometry in the Large -- Differential Geometry of Surfaces in the Small -- Some General Remarks on Closed Surfaces in Differential Geometry -- The Total Curvature (Curvatura Inteqra) of a Closed Surface with Riemannian Metric and Poincarรฉโs Theorem on the Singularities of Fields of Line Elements -- Hadamardโs Characterization of the Ovaloids -- Closed Surfaces with Constant Gauss Curvature (Hilbertโs Method) โ Generalizations and Problems โ General Remarks on Weinqarten Surfaces -- General Closed Surfaces of Genus O with Constant Mean Curvature โ Generalizations -- Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature โ Generalizations -- The Congruence Theorem for Ovaloids -- Singularities of Surfaces with Constant Negative Gauss Curvature